SOLUTION: Simplify the following expression. x^2+x+7/(x-3)(x+4) - x^2+3/(x^2+x-12) I don't understand how to do these types of problems. Help!

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Question 560333: Simplify the following expression. x^2+x+7/(x-3)(x+4) - x^2+3/(x^2+x-12) I don't understand how to do these types of problems. Help!
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Simplify the following expression.
x^2+x+7/(x-3)(x+4) - (x^2+3)/(x^2+x-12)
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Note x^2+x-12 = (x-3)(x+4) so the denominators are the same.
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Combine the numerators over the commondenominator:
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= [x^2+x+7-x^2-3]/lcd
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= (x+4)/[(x-3)(x+4)]
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= 1/(x-3)
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Cheers,
Stan H.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your equation is:
(x^2+x+7)/((x-3)*(x+4)) - (x^2+3)/(x^2+x-12)
x^2 + x -12 can be factored as (x-3)*(x+4)
your equation becomes:
x^2+x+7/(x-3)(x+4) - x^2+3/(x-3)*(x+4))
since the denominators are common, you can combine the numerators under the common denominator to get:
((x^2+x+7)-(x^2 + 3)) / ((x-3)*(x+4))
you can simplify the numerator by removing parentheses to get:
(x^2+x+7-x^2-3) / ((x-3)*(x+4))
simplify this further by combining like terms to get:
(x+4) / ((x-3)*(x+4))
the (x+4) in the numerator and denominator cancel out and you are left with:
1 / (x-3)
your original equation was:
(x^2+x+7)/((x-3)*(x+4)) - (x^2+3)/(x^2+x-12)
your final simplified equation is:
1 / (x-3)
you can confirm that you did it correctly by assuming a value for x and solving for that value in both the original equation and the final equation.
stay away from values that make the denominator equal to 0.
x = 3 would be one such value.
try x = 6.
the final equation would resolve to:
1 / (6-3) = 1/3
the original equation of:
(x^2+x+7)/((x-3)*(x+4)) - (x^2+3)/(x^2+x-12) would resolve to:
(6^2+6+7)/((6-3)*(6+4)) - (6^2+3)/(6^2+6-12) which would simplify to:
(49/30) - (39/30) which would simplify to:
(10/30) which becomes:
1/3
both original equation and simplified equation yield the same result so the solution is assumed to be good.
the final simplified equation is:
1 / (x-3)