Question

How do you solve `\frac { 1} { x - 3} - \frac { 6} { x + 3} = \frac { 1} { x ^ { 2} - 9}`?

Answer 1

Multiply both sides by a factor that removes all of the denominators.

Explanation:

Given: `\frac { 1} { x - 3} - \frac { 6} { x + 3} = \frac { 1} { x ^ { 2} - 9}`

Please observe that `(x+3)(x-3) = x^2-9`, therefore, we can eliminate all of the denominators, if we multiply both sides of the equation by `(x+3)(x-3)`:

`x+3 - 6(x-3) = 1`

Use the distributive property:

`x+3 - 6x+18 = 1`

Combine like terms:

`-5x = -20`

`x = 4`

Check:

`1/(4-3)-6/(4+3)=1/(4^2-9)`

`1-6/7=1/(16-9)`

`7/7-6/7=1/7`

This checks.