SOLUTION: Simplify {{{(x^2+4x+3)/(x^2+7x+12)-(x^2+5x+4)/(x^2-3x-4)}}} please show steps

Question 550674: Simplify please show steps
Found 2 solutions by JBarnum, stanbon:
Answer by JBarnum(2146) (Show Source): You can put this solution on YOUR website!
find the two numbers that multiply to get C and add to get B in each expression
1&3 1*3=3 1+3=4
4&3 4+3=12 4+3=7
1&4 1*4=4 1+4=5
1&-4 1*-4=-4 1+-4=-3
locate the 1s
canceled out the 1s
multiply both fractions by the 1/1 that make a commom denomonator

foil
add like terms
multiply in the -1
add like terms

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Simplify (x^2+4x+3)/(x^2+7x+12)-(x^2+5x+4)/(x^2-3x-4) please show steps
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Factor where you can to get:
[(x+3)(x+1)/(x+3)(x+4)] - [(x+4)(x+1)/(x-4)(x+1)]
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Simplify each fraction:
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= [(x+1)/(x+4)] - [(x+4)/(x-4)]
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= [(x+1)(x-4)-(x^2+8x+16)/(x^2-16)
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= [x^2-3x-4-x^2-8x-16]/(x^2-16)
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= (-11x-20]/[x^2-16]
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Cheers,
Stan H.
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