Question 86485
Simplifying rational expressions:
{{{(x)/(x^2+5x+6)-(2)/ (x^2+3x+2))}}}
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{{{(x)/(x+3)(x+2)-(2)/ (x+1)(x+2)))}}} [factor]
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{{{(x)(x+1)(x+2)/(x+3)(x+2)-(2)(x+3)(x+2)/ (x+1)(x+2)))}}} [cross-multiply]
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{{{(x)(x+1)/(x+3)-(2)(x+3)/ (x+1))))}}} [cancel wherever possible]
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{{{(x^2+x)/(x+3)-(2x+6)/ (x+1)))}}} [simplify the numerators and eliminate the denominator]
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{{{(x^2+x)-(2x+6))))}}}[place the numerator over the LCD (x+3)(x+2)(x+1)]
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{{{(x^2+x -2x-6)/(x+3)(x+2)(x+1))))}}} [combine like-terms in the numerator]
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{{{(x^2 -x-6)/(x+3)(x+2)(x+1))))}}} [simplify]
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{{{((x -3)(x+2))/(x+3)(x+2)(x+1))))}}} [factor the numerator if possible]
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{{{(x -3)/(x+3)(x+1))))}}} [cancel wherever possible]