How do you divide \frac { 2v + 5} { 4v ^ { 4} - v ^ { 2} } \div \frac { 2v + 5} { 4v ^ { 2} - 1}2v+54v4v2÷2v+54v21?

1 Answer
Jul 5, 2017

(4v^2-1)/(4v^4-v^2)4v214v4v2

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))2v+54v4v22v+54v21

Simplify:
((2v+5)/(4v^4-v^2))/((2v+5)/(4v^2-1))2v+54v4v22v+54v21 = ((4v^2-1)(2v+5))/((4v^4-v^2)(2v+5))(4v21)(2v+5)(4v4v2)(2v+5)

Cancel out like terms:
((2v+5)/(4v^4-v^2))/((2v+5)/(4v^2-1))2v+54v4v22v+54v21 = ((4v^2-1)cancel((2v+5)))/((4v^4-v^2)cancel((2v+5)))

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