What is x/(x^2-16)-8/(x^2+5x+4) ?

The solution to x/(x^2-16)-8/(x^2+5x+4) is (x^2-7x+32)/((x+4)(x-4)(x+1))

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simplify x/(x^2-16)-8/(x^2+5x+4)

simplify

\frac{x}{x ^{2} - 16} - \frac{8}{x ^{2} + 5 x + 4}

\frac{x ^{2} - 7 x + 32}{( x + 4 ) ( x - 4 ) ( x + 1 )}

Solution steps

\frac{x}{x ^{2} - 16} - \frac{8}{x ^{2} + 5 x + 4}

Least Common Multiplier of

x^{2} - 16, x^{2} + 5 x + 4 : (x + 4) (x - 4) (x + 1)

Adjust Fractions based on the LCM

= \frac{x ( x + 1 )}{( x + 4 ) ( x - 4 ) ( x + 1 )} - \frac{8 ( x - 4 )}{( x + 4 ) ( x - 4 ) ( x + 1 )}

Apply the fraction rule:

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

= \frac{x ( x + 1 ) - 8 ( x - 4 )}{( x + 4 ) ( x - 4 ) ( x + 1 )}

Simplify

x (x + 1) - 8 (x - 4) : x^{2} - 7 x + 32

= \frac{x ^{2} - 7 x + 32}{( x + 4 ) ( x - 4 ) ( x + 1 )}

125 b

\frac{x ^{2} - 2 x - 3}{x ^{2} - x - 2}

(3 x - \frac{1}{2})^{2}

(a - x)^{3}

4 x^{2} + x^{2}

What is x/(x^2-16)-8/(x^2+5x+4) ?
The solution to x/(x^2-16)-8/(x^2+5x+4) is (x^2-7x+32)/((x+4)(x-4)(x+1))