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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

partialfraction x/(x^2-1)

partial fractions

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

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

Solution steps

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

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 )}

x \to 5 lim (x^{2})

x \to \infty lim ((x)!)

π^{3}

\int_{1}^{\infty} \frac{4}{x ^{2} + 1} d x

\int 8 e^{8 x} sin (e^{8 x}) d x

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