## Related questions with answers

Write the partial fraction decomposition for the rational expression. Check your result algebraically by combining fractions, and check your result graphically by using a graphing utility to graph the rational expression and the partial fractions in the same viewing window. $\frac{1}{x^{2}+x}$

Solutions

VerifiedWe need to write the partial fraction decomposition for the rational expression

$\dfrac{1}{x^{2}-1}$

$\begin{align*} \dfrac{1}{x^2 - 1}&= \dfrac{A}{x -1 } + \dfrac{B}{x+1}\\ &= \dfrac{A(x+1) + B(x-1)}{x^2 - 1}\\ 1 &= A(x+1) + B(x-1)\\ &= Ax + A + Bx - B\\ 0 \cdot x + 1 &= (A+B)x + (A-B)\\ \\ A+B &= 0\\ A-B &= 1\\ \end{align*}$

Use the factors of the denominator to write each partial fraction.

Combine the partial fractions with a common denominator.

Multiply it out into a polynomial, then form a system of equations by equating corresponding coefficients of each side of the "=" sign.

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Principles of Mathematics 10

1st Edition•ISBN: 9780070973329Brian McCudden, Chris Dearling, Wayne Erdman#### Algebra and Trigonometry: Structure and Method, Book 2

1st Edition•ISBN: 9780395977255 (2 more)Brown, Dolciani, Kane, Sorgenfrey#### Cambridge IGCSE Mathematics: Core and Extended

3rd Edition•ISBN: 9781444191707Ric Pimentel## More related questions

1/4

1/7