Question

How do you subtract `1/(x-6) - 3/(x+6) + (3x)/(36-x^2)`?

Answer 1

`1/(x-6)-3/(x+6)+(3x)/(36-x^2)=(24-5x)/(x^2-36)`

Explanation:

`1/(x-6)-3/(x+6)+(3x)/(36-x^2)`

= `1/(x-6)-3/(x+6)-(3x)/(x^2-36)`

As GCD of `(x-6)`, `(x+6)` and `(x^2-36)` is `(x^2-36)=(x-6)(x+6)`, above can be written as

`((x+6)-3(x-6)-3x)/(x^2-36)`

= `(x+6-3x+18-3x)/(x^2-36)`

= `(24-5x)/(x^2-36)`