What is partialfraction x/(x^2-9) ?

The solution to partialfraction x/(x^2-9) is 1/(2(x+3))+1/(2(x-3))

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partialfraction x/(x^2-9)

partial fractions

\frac{x}{x ^{2} - 9}

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

Solution steps

\frac{x}{x ^{2} - 9}

Factor

x^{2} - 9 : (x + 3) (x - 3)

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

Create the partial fraction template using the denominator

(x + 3) (x - 3)

\frac{x}{( x + 3 ) ( x - 3 )} = \frac{a _{0}}{x + 3} + \frac{a _{1}}{x - 3}

Multiply equation by the denominator

\frac{x ( x + 3 ) ( x - 3 )}{( x + 3 ) ( x - 3 )} = \frac{a _{0} ( x + 3 ) ( x - 3 )}{x + 3} + \frac{a _{1} ( x + 3 ) ( x - 3 )}{x - 3}

Simplify

x = a_{0} (x - 3) + a_{1} (x + 3)

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

- 3, 3

For the denominator root

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

For the denominator root

3 : 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 + 3} + \frac{\frac{1}{2}}{x - 3}

Simplify

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

\frac{d}{d y} (sinh (y))

x^{2} + 11 x y + y^{2} = 11

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

\frac{d}{d x} (3 lo g_{10} (x))

\frac{\partial}{\partial x} (\frac{1}{2 x + 4 y ^{2}})

What is partialfraction x/(x^2-9) ?
The solution to partialfraction x/(x^2-9) is 1/(2(x+3))+1/(2(x-3))