Question

How do you combine `\frac { 3v } { v + 3} + \frac { 5} { 2v - 1}` into one fraction?

Answer 1

`= (6v^2+2v+15)/(2v^2+5v-3)`

Explanation:

For two or more fractions to be combined, they must have the same denominator.

To make this the case, find the LCM of the denominators.
(in this case, multiply them)

`LCM (v+3),(2v-1) = (v+3)(2v-1)`

`(v+3)(2v-1)=2v^2-v+6v-3`

`=2v^2+5v-3`

Then multiply the numerators:

`(3v)/(v+3) = (3v(2v-1))/(2v^2+5v-3)`

`rArr=(6v^2-3v)/(2v^2+5v-3)`

`(5)/(2v-1) = (5(v+3))/(2v^2+5v-3)`

`rArr= (5v+15)/(2v^2+5v-3)`

Now add the two fractions together:

`(6v^2-3v)/(2v^2+5v-3)+ (5v+15)/(2v^2+5v-3)`

`= (6v^2+2v+15)/(2v^2+5v-3)`