Question

How do you simplify `\frac { v ^ { 2} - v - 30} { 7v - 42} \cdot \frac { 6v ^ { 3} + 48v ^ { 2} } { 6v ^ { 3} + 30v ^ { 2} }`?

Answer 1

`=(v+8)/7`

Explanation:

Factorise wherever you can.

`(v^2-v-30)/(7v-42) xx (6v^3+48v^2)/(6v^3+30v^2)`

`= ((v-6)(v+5))/(7(v-6) ) xx (6v^2(v+8))/(6v^2(v+5))`

Cancel the like factors:

`= (cancel((v-6))cancel((v+5)))/(7cancel((v-6)) ) xx (cancel(6v^2)(v+8))/(cancel(6v^2)(cancel(v+5)))`

`=(v+8)/7`