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

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

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partialfraction x/(1-x^2)

partial fractions

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

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

Solution steps

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

Factor

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

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

Create the partial fraction template using the denominator

- (x + 1) (x - 1)

\frac{x}{- ( x + 1 ) ( x - 1 )} = \frac{a _{0}}{x + 1} + \frac{a _{1}}{x - 1}

Multiply equation by the denominator

\frac{x ( - ( x + 1 ) ( x - 1 ) )}{- ( x + 1 ) ( x - 1 )} = \frac{a _{0} ( - ( x + 1 ) ( x - 1 ) )}{x + 1} + \frac{a _{1} ( - ( x + 1 ) ( x - 1 ) )}{x - 1}

Simplify

x = - a_{0} (x - 1) - a_{1} (x + 1)

Solve the unknown parameters by plugging the real roots of the denominator:

- 1, 1

For the denominator root

- 1 : a_{0} = - \frac{1}{2}

For the denominator root

1 : a_{1} = - \frac{1}{2}

a_{0} = - \frac{1}{2}, a_{1} = - \frac{1}{2}

Plug the solutions to the partial fraction parameters to obtain the final result

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

Simplify

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

f (x) = 8 x

\frac{d}{d x} (lo g_{3} (x e^{x}))

y = (x^{3} - 4 x)^{8}, (2, 0)

\frac{d}{d t} (\frac{e ^{t b} - e ^{t a}}{t ( b - a )})

y^{^{''}} + 9 y = 12 sin (3 t)

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