What is 2/(x^2-4)-3/(x^2+5x+6) ?

The solution to 2/(x^2-4)-3/(x^2+5x+6) is (-x+12)/((x+2)(x-2)(x+3))

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simplify 2/(x^2-4)-3/(x^2+5x+6)

simplify

\frac{2}{x ^{2} - 4} - \frac{3}{x ^{2} + 5 x + 6}

\frac{- x + 12}{( x + 2 ) ( x - 2 ) ( x + 3 )}

Solution steps

\frac{2}{x ^{2} - 4} - \frac{3}{x ^{2} + 5 x + 6}

Least Common Multiplier of

x^{2} - 4, x^{2} + 5 x + 6 : (x + 2) (x - 2) (x + 3)

Adjust Fractions based on the LCM

= \frac{2 ( x + 3 )}{( x + 2 ) ( x - 2 ) ( x + 3 )} - \frac{3 ( x - 2 )}{( x + 2 ) ( x - 2 ) ( x + 3 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{2 ( x + 3 ) - 3 ( x - 2 )}{( x + 2 ) ( x - 2 ) ( x + 3 )}

Simplify

2 (x + 3) - 3 (x - 2) : - x + 12

= \frac{- x + 12}{( x + 2 ) ( x - 2 ) ( x + 3 )}

\frac{1}{56} \div \frac{7}{8}

33 - 23

x^{6} - 3 x^{5} - 3 x^{4} - 5 x^{3} + 2 x^{2} + 8 x

\frac{11}{10}

\frac{- 9}{25}

What is 2/(x^2-4)-3/(x^2+5x+6) ?
The solution to 2/(x^2-4)-3/(x^2+5x+6) is (-x+12)/((x+2)(x-2)(x+3))