What is (2x)/(x^2-1)-3/(x^2+5x+4) ?

The solution to (2x)/(x^2-1)-3/(x^2+5x+4) is (2x+3)/((x-1)(x+4))

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simplify (2x)/(x^2-1)-3/(x^2+5x+4)

simplify

\frac{2 x}{x ^{2} - 1} - \frac{3}{x ^{2} + 5 x + 4}

\frac{2 x + 3}{( x - 1 ) ( x + 4 )}

Solution steps

\frac{2 x}{x ^{2} - 1} - \frac{3}{x ^{2} + 5 x + 4}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{2 x ( x + 4 )}{( x + 1 ) ( x - 1 ) ( x + 4 )} - \frac{3 ( x - 1 )}{( x + 1 ) ( x - 1 ) ( x + 4 )}

Apply the fraction rule:

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

= \frac{2 x ( x + 4 ) - 3 ( x - 1 )}{( x + 1 ) ( x - 1 ) ( x + 4 )}

Simplify

2 x (x + 4) - 3 (x - 1) : 2 x^{2} + 5 x + 3

= \frac{2 x ^{2} + 5 x + 3}{( x + 1 ) ( x - 1 ) ( x + 4 )}

Cancel

\frac{2 x ^{2} + 5 x + 3}{( x + 1 ) ( x - 1 ) ( x + 4 )} : \frac{2 x + 3}{( x - 1 ) ( x + 4 )}

= \frac{2 x + 3}{( x - 1 ) ( x + 4 )}

- a \cdot a

sin^{2} (x) + cos^{2} (x)

\frac{12 + r - r ^{2}}{r ^{3} + 3 r ^{2}}

\frac{5}{6 x ^{8}} - \frac{1}{7 x ^{5}}

\frac{1}{2} + \frac{1}{3} + \frac{1}{8}

What is (2x)/(x^2-1)-3/(x^2+5x+4) ?
The solution to (2x)/(x^2-1)-3/(x^2+5x+4) is (2x+3)/((x-1)(x+4))