What is x/(x^2-3x-4)-(x+3)/(x^2-1) ?

The solution to x/(x^2-3x-4)-(x+3)/(x^2-1) is (12)/((x+1)(x-4)(x-1))

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simplify x/(x^2-3x-4)-(x+3)/(x^2-1)

simplify

\frac{x}{x ^{2} - 3 x - 4} - \frac{x + 3}{x ^{2} - 1}

\frac{12}{( x + 1 ) ( x - 4 ) ( x - 1 )}

Solution steps

\frac{x}{x ^{2} - 3 x - 4} - \frac{x + 3}{x ^{2} - 1}

Least Common Multiplier of

x^{2} - 3 x - 4, x^{2} - 1 : (x + 1) (x - 4) (x - 1)

Adjust Fractions based on the LCM

= \frac{x ( x - 1 )}{( x + 1 ) ( x - 4 ) ( x - 1 )} - \frac{( x + 3 ) ( x - 4 )}{( x + 1 ) ( x - 4 ) ( x - 1 )}

Apply the fraction rule:

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

= \frac{x ( x - 1 ) - ( x + 3 ) ( x - 4 )}{( x + 1 ) ( x - 4 ) ( x - 1 )}

Simplify

x (x - 1) - (x + 3) (x - 4) : 12

= \frac{12}{( x + 1 ) ( x - 4 ) ( x - 1 )}

\frac{77}{10}

\frac{2}{1} \times \frac{3}{2}

\frac{15 x ^{2} y ^{2}}{25 x y ^{7}}

+ \frac{14}{13} \cdot (- 4)

What is x/(x^2-3x-4)-(x+3)/(x^2-1) ?
The solution to x/(x^2-3x-4)-(x+3)/(x^2-1) is (12)/((x+1)(x-4)(x-1))