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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

3 (x - 3) + 5 : 3 x - 4

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

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

(6 r - 1) (- 8 r - 3)

3 a (8 a - 6 b)

- a^{4} + 4 - 9 a^{4} - 3 - 4 a^{2}

\frac{a ^{2} + 2 a - 3}{a ^{2} + 4 a - 5}

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