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

The solution to x/(x^2-16)-5/(x^2+5x+4) is (x^2-4x+20)/((x+4)(x-4)(x+1))

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

simplify

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

\frac{x ^{2} - 4 x + 20}{( x + 4 ) ( x - 4 ) ( x + 1 )}

Solution steps

\frac{x}{x ^{2} - 16} - \frac{5}{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{5 ( 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 ) - 5 ( x - 4 )}{( x + 4 ) ( x - 4 ) ( x + 1 )}

Simplify

x (x + 1) - 5 (x - 4) : x^{2} - 4 x + 20

= \frac{x ^{2} - 4 x + 20}{( x + 4 ) ( x - 4 ) ( x + 1 )}

\frac{1 + tan ^{2} ( x )}{csc ^{2} ( x )}

\frac{a ^{2} b}{5} - \frac{2 a b ^{2}}{3} + \frac{3 a b ^{2}}{2} - \frac{6 a ^{2} b}{5}

22 m^{7} \cdot 8 m^{2}

6 (x + 4)

(a + b) (a + c) (b + c)

What is x/(x^2-16)-5/(x^2+5x+4) ?
The solution to x/(x^2-16)-5/(x^2+5x+4) is (x^2-4x+20)/((x+4)(x-4)(x+1))