Question

How do you add `\frac { 4x } { 3x - 1} + \frac { 9} { x + 4}`?

Answer 1

`(4x^2+43x-9)/((3x-1)(x+4))`

Explanation:

The denominators must be the same in order to add fractions.

`(4x)/(3x-1)(x+4)/(x+4)+(3x-1)/(3x-1)9/(x+4)`

`(4x^2+16x)/((3x-1)(x+4))+(27x-9)/((3x-1)(x+4))`

`(4x^2+16x+27x-9)/((3x-1)(x+4))`

`(4x^2+43x-9)/((3x-1)(x+4))`

Because the numerator does not factor (at least not to anything nicely), this completes the addition.