# How do you simplify #(2-1/y)/(4-1/ y^2)#?

##### 2 Answers

Sep 22, 2015

It is

Sep 22, 2015

Multiply both numerator and denominator by

#(2-1/y)/(4-1/(y^2)) = y/(2y+1)#

with exclusions

#### Explanation:

#f(y) = (2-1/y)/(4-1/(y^2)) = ((2y-1)y)/(4y^2-1) = ((2y-1)y)/((2y)^2 - 1^2)#

#= ((2y-1)y)/((2y-1)(2y+1)) = y/(2y+1)#

with exclusions

Notice that if