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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

2 x + x + 1 + x - 1 : 4 x

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

r (3 r^{2} - s) + s (r - r^{4})

(27 x^{- 3})^{\frac{1}{3}}

5 y^{2} - 8 y + 2 - 3 y^{2} + 3 y

(x^{x})^{2} - 3 + ((x - 3)^{x})^{2}

\frac{q ^{8}}{q ^{19}}

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