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

The solution to 1/(x^2+4x+3)+3/(x^2-1)-2/(x+3) is (-2x^2+4x+10)/((x+1)(x+3)(x-1))

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

simplify

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

\frac{- 2 x ^{2} + 4 x + 10}{( x + 1 ) ( x + 3 ) ( x - 1 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x - 1 + 3 (x + 3) - 2 (x + 1) (x - 1) : - 2 x^{2} + 4 x + 10

= \frac{- 2 x ^{2} + 4 x + 10}{( x + 1 ) ( x + 3 ) ( x - 1 )}

3 (x - 2) + 2 (4 x - 1)

36 x^{5}

(0.7)^{2}

- 3 (4)

\frac{5 x}{5}

What is 1/(x^2+4x+3)+3/(x^2-1)-2/(x+3) ?
The solution to 1/(x^2+4x+3)+3/(x^2-1)-2/(x+3) is (-2x^2+4x+10)/((x+1)(x+3)(x-1))