Question

How do you solve `\frac { 1} { u - 2} + \frac { 6} { u ^ { 2} - 4} = \frac { 3} { u + 2}`?

Answer 1

`u=7`

Explanation:

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

Now, `(u^2-4)` can also be written as `(u-2)(u+2)`. Hence,

`1/(u-2)+6/((u-2)(u+2))=3/(u+2)`

Multiply all terms by `(u-2)(u+2)`.

`1/(u-2)xx(u-2)(u+2)+6/((u-2)(u+2))xx(u-2)(u+2)=3/(u+2)xx(u-2)(u+2)`

`1/(1cancel((u-2)))xx1cancel((u-2))(u+2)+6/(1cancel((u-2)(u+2)))xx1cancel((u-2)(u+2))=3/(1cancel((u+2)))xx(u-2)1cancel((u+2))`

`1xx(u+2)+6=3xx(u-2)`

Open the brackets and simplify.

`u+2+6=3u-6`

Add `6` to both sides.

`u+2+6+6=3u-6+6`

`u+14=3u`

Subtract `u` from each side.

`u-u+14=3u-u`

`14-2u`

Divide both sides by `2`.

`7=u` or `u=7`