Question 126848
Given:
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{{{x^2/(x-2) = 4/(x-2)}}}
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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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{{{((x-2)*x^2)/(x-2) = ((x-2)*4)/(x-2)}}}
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Then cancel the {{{x-2}}} terms in the numerators with the same terms in the denominators:
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{{{(cross(x-2)*x^2)/cross(x-2) = (cross(x-2)*4)/cross(x-2)}}}
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What you are left with is:
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{{{x^2 = 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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{{{(-2)^2/(-2-2) = 4/(-2-2)}}}
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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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{{{(-2)^2/(-4) = 4/(-4)}}}
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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/(-4) = 4/(-4)}}}
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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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