Question 125794: Please Help! I can not figure this out.
Solve
5 OVER x MINUS x-3 OVER x+2 = 22 OVER x squared + 2x Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Given:
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First factor the denominator on the right side and you get:
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Now you can simplify the whole equation by multiplying both sides (all terms) by the common
denominator of x*(x + 2). When you do that multiplication the equation becomes:
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Then cancel any common terms in the numerators with the corresponding identical terms in the
denominators as follows:
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and this reduces the equation to:
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Do the distributed multiplications and it becomes:
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Combine like terms on the left side to get:
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Subtract 22 from both sides to make the right side = 0
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and to simplify things, make the squared term + by multiplying the entire equation (all terms
on both sides) by -1 to get:
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This equation can be factored to get:
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and this equation will be true if either of the two factors on the left side equals zero
because a multiplication by zero on the left side will make the entire left side become zero and
therefore it will equal the right side. So one at a time, set the factors equal to zero and
solve for the value of x that will do that ...
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By adding 6 to both sides you get
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Next set the other factor equal to zero:
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and by adding 2 to both sides you find that
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So the two answers to the original problem you were given are x = 6 and x = 2.
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You can check both answers by substituting them into the original equation you were given and
determining if the equation works out. We'll do it for x = 6 .... Start with:
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Replace x with 6 and this becomes:
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Combine the numbers in parentheses and calculate the denominator on the right side to get:
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Combine the numbers in the denominator on the right side:
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Put all terms over a common denominator of 48:
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Multiply out the numerators on the right side:
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Since the two terms on the left side have a common denominator of 48, you can combine their
numerators over the common denominator to get:
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And combining the numerators on the left side results in:
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Since both sides are equal you can say that x = 6 is an answer that works. I'll leave it up
to you to perform a similar check for x = 2.
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Hope this helps you to see your way through the problem.
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