document.write( "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.
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Algebra.Com's Answer #92917 by bucky(2189) $\"\"$ $\"About$

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