SOLUTION: {{{x^2/x-2=4/x-2}}} I don't know if I typed this question out right. It should be x squared over x-2 = 4 over x-2. And the instructions are to solve for x. Thank you shelena

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{x^2/x-2=4/x-2}}} I don't know if I typed this question out right. It should be x squared over x-2 = 4 over x-2. And the instructions are to solve for x. Thank you shelena      Log On


   

Question 126848: x%5E2%2Fx-2=4%2Fx-2 I don't know if I typed this question out right. It should be x squared over x-2 = 4 over x-2. And the instructions are to solve for x.
Thank you
shelena
Found 2 solutions by MathLover1, bucky:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2F%28x-2%29=4%2F%28x-2%29 ....if denominators are same, then nominators must be too if we have equal sign, so you have:
x%5E2=4
x+=+sqrt%284%29
x1=2
x2=-2

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
x%5E2%2F%28x-2%29+=+4%2F%28x-2%29
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Since the denominators of both terms are x-2 we can get rid of them by multiplying
both sides of this equation by the quantity x-2. That multiplication leads to:
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%28%28x-2%29%2Ax%5E2%29%2F%28x-2%29+=+%28%28x-2%29%2A4%29%2F%28x-2%29
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Then cancel the x-2 terms in the numerators with the same terms in the denominators:
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%28cross%28x-2%29%2Ax%5E2%29%2Fcross%28x-2%29+=+%28cross%28x-2%29%2A4%29%2Fcross%28x-2%29
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What you are left with is:
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x%5E2+=+4
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To solve, take the square root of both sides to get two possible answers:
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x+=+2 and x+=+-2
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because if either 2 or -2 is squared, the result is +4.
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We need to check out these two answers. Let's look first at x = +2. Go to the original
problem and substitute +2 for x. oops. Notice what happens. Both terms have (x - 2) in the
denominator. When x is +2 and you subtract 2 from it, the denominator becomes 0. But division
by zero is not allowed in algebra. Therefore, x cannot equal +2.
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What about if x = -2. If we substitute -2 for x in the original problem, it becomes:
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%28-2%29%5E2%2F%28-2-2%29+=+4%2F%28-2-2%29
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(-2 - 2) is equal to -4. So we can substitute -4 for both of the denominators to get:
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%28-2%29%5E2%2F%28-4%29+=+4%2F%28-4%29
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Then you can note that squaring -2 results in +4. You can substitute +4 for the numerator on
the left side. When you do that substitution the equation becomes:
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4%2F%28-4%29+=+4%2F%28-4%29
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Without going further, you can see that the left side equals the right side. Therefore,
if you take -2 as the value of x, it will maintain the equality of both sides of the equation.
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Therefore, the answer to your problem is x = -2.
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Hope this helps you to understand the problem and to see the procedures that you can use to
solve it.
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