Log in Griffin Forsgren 12 years agoPosted 12 years ago. Direct link to Griffin Forsgren's post “At 1:36, couldn't you jus...” At • (10 votes) Ryuudo 12 years agoPosted 12 years ago. Direct link to Ryuudo's post “when you do sq in the cal...” when you do sq in the calculator you only get the positive half of the root, you need to remember it could also equal the negative number. bottom line: you could. :) (14 votes) Bobby Smith 12 years agoPosted 12 years ago. Direct link to Bobby Smith's post “Why is x=-2 not a possibi...” Why is x=-2 not a possibility? even though 4/0 is 0 it is still zero. I understand that is different but I need to organize this better in my mind. Can someone please explain better? • (3 votes) Cesar S 11 years agoPosted 11 years ago. Direct link to Cesar S's post “4/0 is equivalent to tryi...” 4/0 is equivalent to trying to divide 4 by 0, which is undefined, and hence why you cannot have it as a solution. (1 vote) Hunter Linton 11 years agoPosted 11 years ago. Direct link to Hunter Linton's post “This may sound a silly qu...” This may sound a silly question but something just occured to me. At first I used a different method to solve this. I was just wondering, if you can somehow reduce an equation like this to another equation with only one solution, would be safe to assume that said solution is non extraneous? Thanks. • (3 votes) Ethan Dlugie 11 years agoPosted 11 years ago. Direct link to Ethan Dlugie's post “The only thing to be wary...” The only thing to be wary of is when you cancel the (x+2) factor from the top and bottom. It was okay for this problem, and you got the right answer. (6 votes) Suhail Khalid 11 years agoPosted 11 years ago. Direct link to Suhail Khalid's post “Is there a way to book ma...” Is there a way to book mark any video ? • (3 votes) ItsSunnyMonster 3 years agoPosted 3 years ago. Direct link to ItsSunnyMonster's post “You can just bookmark the...” You can just bookmark the page in your browser. Make sure that you are on the page of the video by clicking the video name on top of the frame (if you see it) :) (1 vote) N 10 years agoPosted 10 years ago. Direct link to N's post “I understand how you can ...” I understand how you can get an extraneous root from difference of perfect squares since the square root of something can be positive or negative. But how come you can get an extraneous solution from a different type of quadratic equation? How can you get an answer from an equation that isn't an answer? If the number is coming from the equation shouldn't it be a solution to it? • (3 votes) Nicolas Posunko 10 years agoPosted 10 years ago. Direct link to Nicolas Posunko's post “The extraneous root here ...” The extraneous root here is also "coming from the equation". Factoring the difference of perfect squares is just how you happen to solve it. With any equation, you simplify it (like when we got rid of the denominators in this case) and then either get a solution/solutions or not. It doesn't matter how you got these solutions, but if you input some "root" into the original equation and it causes you to perform some invalid operation—like division by zero—it's not a proper root, the equation breaks down with it. It happens because as you go about simplifying the original equation, the information about values that are just out of consideration is lost or they become less obvious. Also, extraneous roots aren't connected to roots that come in pairs (You said, "I understand... ...since the square root can be positive or negative.") One can probably imagine some more exotic case where you get a single root and it's an extraneous one; OR where you get two extraneous roots. (4 votes) James 12 years agoPosted 12 years ago. Direct link to James's post “At 0:48 Sal says that x c...” At (-2)^2/(-2+2) = 4/(-2+2) Why it isn't a solution ? Yeah, we don't know what is the quotient of 4/0, but, isn't it logical to assume that whatever the quotient is, it is going to be equal to 4/0? I mean, they're both the same thing. (4/0 = 4/0) • (2 votes) Seth 12 years agoPosted 12 years ago. Direct link to Seth's post “4/0 is undefined (in a wa...” 4/0 is undefined (in a way, its not even a number), so it can't be a solution and if you try to solve it with 4/0 your equation will just be messed up. There are contexts where it is defined, but they don't usually appear until much later in your math studies. (5 votes) Among.36 11 years agoPosted 11 years ago. Direct link to Among.36's post “I`d like to receive an ex...” I • (2 votes) Noble Mushtak 11 years agoPosted 11 years ago. Direct link to Noble Mushtak's post “Since there are multiple ...” Since there are multiple ways to solve this equation, some of them might not include extraneous solutions. Your other way of solving the equation is just as correct and okay as Sal's way even though it does not show any extraneous solutions. I hope this helps! (3 votes) Charlotte Orr 10 years agoPosted 10 years ago. Direct link to Charlotte Orr's post “In the earlier video Rati...” In the earlier video Rational equations, Sal discusses excluded values. The excluded value is excluded as it would make the denominator 0. Is this the same thing as the extraneous solution? The words are interchangeable? Thanks! • (2 votes) Christopher Blake 10 years agoPosted 10 years ago. Direct link to Christopher Blake's post “Not exactly. Excluded va...” Not exactly. Excluded values are values that are not in the domain - values that would not be okay to "plug in" because they would cause us to have a 0 in the bottom of a fraction. Extraneous solutions are results that you might get from your work that need to be thrown away because they happen to be one of the excluded values. It's a bit of a misnomer because "extraneous solutions" are not really solutions at all. (2 votes) Brooke 11 years agoPosted 11 years ago. Direct link to Brooke's post “At around 1:40, couldn't ...” At around • (2 votes) Christian 8 years agoPosted 8 years ago. Direct link to Christian's post “Why is negative 2 not a s...” Why is negative 2 not a solution when 2 is? They both give the same answer. Why is 2 not an extraneous solution then? • (1 vote) Kim Seidel 8 years agoPosted 8 years ago. Direct link to Kim Seidel's post “Let's do the checks for e...” Let's do the checks for each value and see which one(s) work. That might make it clearer. Here is the check for X=2: Here is the check for X = -2 Hope this helps. (2 votes)Want to join the conversation?
1:36
(x^2 / (x+2)) - (4 / (x+2)) = 0
(x^2 - 4) / (x+2) = 0
(x+2)(x-2) / (x + 2) = 0
x - 2 = 0
x = 2
But you must be careful. Let's say that after you cancelled, you were left with (x-2)*(x+2)=0. You would think that the solutions were x=2 and x=-2. However, if you plug -2 into the original problem, your answer would be indeterminate.
The safest thing to do is to append a note x≠-2 after you cancel the (x+2) factor. 0:48
But, I still don't get it:
4/0 = 4/0d like to receive an explanation for some other way of solving the problem. Assume that we do not multiply both sides by (x+2), but rather move 4/(x+2) to the left side, so we get (x^2-4)/(x+2) = 0. We can factor x^2-4 as a difference of squares to receive (x+2)(x-2) and then cancel out x+2 in both nominator and denominator, setting a domain of all real numbers except x=-2. Well get x-2=0, x=2. As a result, there is NO extraneous solution, there is only one (x=2), while the other one appears to be a restriction, not an extraneous solution.
Can you explain me this? Is it okay that solving an equation the way I propose you fail to find an extraneous solution, instead of this putting a restriction for the domain practically from the start? 1:40
The equation is: X^2 / (X+2) = 4 / (X+2)
2^2 / (2+2) = 4 / (2+2)
4 / 4 = 4 / 4
1 = 1 The 2 sides match and neither side is undefined. So X=2 is an acceptable solution.
(-2)^2 / (-1+2) = 4 / (-1+2)
4 / 0 = 4 / 0
While the 2 sides are the same, they both have division by 0. This is undefined. So, X = -2, is not an acceptable solution. It is considered extraneous because it creates these undefined states which are not allowed.
FAQs
What are 5 examples of rational equations? ›
- 4/x + 5/2 = -11/x.
- 5x/(x - 2) = 7 + 10/(x - 2)
- ( 3x - 2)/(x - 2) = 6/(x2 - 4) + 1.
- 2/(x2 - x) = 1/(x - 1)
- 3/(x + 2) = 6/(x - 1)
- Write all fractions as equivalent fractions with a common denominator.
- Combine the fractions as a single fraction that has the common denominator.
- Simplify the expression in the top of the fraction.
- Reduce the fraction to lowest terms.
A rational expression is simply a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials. These are examples of rational expressions:
What is the difference between a rational function and a rational equation? ›A rational equation is an equation that contains a rational expression. A rational expression is an expression of the form pq, where p and q are polynomials and q≠0. A rational function is a function of the form R(x)=p(x)q(x) where p(x) and q(x) are polynomial functions and q(x) is not zero.
What are 2 examples of rational algebraic expression? ›RATIONAL ALGEBRAIC EXPRESSION: Just for your own benefit, we define a rational number as a number expressed in the form of p/q where it is not equal to zero. ... Examples of rational expression are 5/x − 2, 4/(x + 1), (x + 5)/5, (x2 + 5x + 4)/(x + 5), (x + 1)/(x + 2), (x2 + x + 1)/2x etc.
What are 10 rational examples? ›Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on. The number “0” is also a rational number, as we can represent it in many forms such as 0/1, 0/2, 0/3, etc. But, 1/0, 2/0, 3/0, etc. are not rational, since they give us infinite values.
What is an example of a rational function and expression? ›Any function of one variable, x, is called a rational function if, it can be represented as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials such that q(x) ≠ 0. For example, f(x) = (x2 + x - 2) / (2x2 - 2x - 3) is a rational function and here, 2x2 - 2x - 3 ≠ 0.
What is rational equation in real life? ›Rational equations can be used to solve a variety of problems that involve rates, times and work. Using rational expressions and equations can help you answer questions about how to combine workers or machines to complete a job on schedule.
How do you know if an equation is a rational expression? ›Definitions: A rational expression is the ratio of two polynomials. If f is a rational expression then f can be written in the form p/q where p and q are polynomials.
What is the formula of a rational equation? ›A rational equation is an equation that contains fractions with xs in the numerator, denominator or both. Here is an example of a rational equation: (4 / (x + 1)) - (3 / (x - 1)) = -2 / (x^2 - 1).
How do you tell if it's a rational function? ›
A rational function is a function that is a fraction and has the property that both its numerator and denominator are polynomials. In other words, R(x) is a rational function if R(x) = p(x) / q(x) where p(x) and q(x) are both polynomials.
What are 5 rational number examples? ›(i) The five rational numbers between -1 and 0 are -5/6 , -2/3 , -1/2 , -1/3 , -1/6 (ii) The five rational numbers between -2 and -1 are -11/6 , -5/3 , -3/2 , -4/3 , -7/6 (iii) The five rational numbers between -4/5 and -2/3 are, -7/9 , -34/45 , -11/15 , -32/45 , -31/45 (iv) The five rational numbers between -1/2 and 2 ...
What are the 5 example of rational inequality? ›A rational inequality is an inequality that contains a rational expression. Inequalities such as 3 2 x > 1 , 2 x x − 3 < 4 , 2 x − 3 x − 6 ≥ x , 3 2 x > 1 , 2 x x − 3 < 4 , 2 x − 3 x − 6 ≥ x , and 1 4 − 2 x 2 ≤ 3 x 1 4 − 2 x 2 ≤ 3 x are rational inequalities as they each contain a rational expression.
What is an example of a rational function equation? ›Any function of one variable, x, is called a rational function if, it can be represented as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials such that q(x) ≠ 0. For example, f(x) = (x2 + x - 2) / (2x2 - 2x - 3) is a rational function and here, 2x2 - 2x - 3 ≠ 0.