Question

How do you divide `\frac { 2v + 5} { 4v ^ { 4} - v ^ { 2} } \div \frac { 2v + 5} { 4v ^ { 2} - 1}`?

Answer 1

`(4v^2-1)/(4v^4-v^2)`

Explanation:

First, we write the division in fraction form (notice: you don't have to do this if you're familiar with division by two fractions):
`((2v+5)/(4v^4-v^2))/((2v+5)/(4v^2-1))`

Simplify:
`((2v+5)/(4v^4-v^2))/((2v+5)/(4v^2-1))` = `((4v^2-1)(2v+5))/((4v^4-v^2)(2v+5))`

Cancel out like terms:
`((2v+5)/(4v^4-v^2))/((2v+5)/(4v^2-1))` = `((4v^2-1)cancel((2v+5)))/((4v^4-v^2)cancel((2v+5)))`

And you get `(4v^2-1)/(4v^4-v^2)`