Question

Split $(4ax-a^2)/(x^2+ax-2a^2)$ into partial fractions.

Answer 1

The decomposition of the partial fraction is $\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}$

How to split the fraction?

The expression is given as:

$\frac{4ax-a^2}{x^2+ax-2a^2}$

Expand the denominator

$\frac{4ax-a^2}{x^2- ax+2ax-2a^2}$

Factorize

$\frac{4ax-a^2}{x(x- a)+2a(x-a)}$

Factor out x - a

$\frac{4ax-a^2}{(x+ 2a)(x-a)}$

The denominator of the partial fraction is a product of two linear factors.

So, the decomposition can be represented as:

$\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}$

Read more about partial fractions at:

https://brainly.com/question/18958301

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