Question

partial fractions.. x/x^2-4

Answer 1

Write it as

\[

\frac{x}{x^2-4}=\frac{A}{x-2}+\frac{B}{x+2}

\]

Answer 2

Find A and B

Answer 3

Multiply the two sides by (x-2) to get
\[
\frac{x (x-2)}{(x-2) (x+2)}=\frac{A (x-2)}{x-2}+\frac{B (x-2)}{x+2}\\
\frac{x}{x+2}=\frac{A}{1}+\frac{B (x-2)}{x+2}
\]
Put x =2 and get A
Do the same for B

Answer 4

thank you

Answer 5

The final answer looks like
\[
\frac{x}{x^2-4}=\frac{1}{2 (x+2)}+\frac{1}{2 (x-2)}
\]

Answer 6

YW

Answer 7

thats the final answer

Answer 8

yes