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

1 Answer
Demirari
Jul 5, 2017

#(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)#

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