How do you simplify #\frac { 4y } { y ^ { 2} - 9} - \frac { 12} { y ^ { 2} - 9}#?

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Answer 1 · 2018-04-22T08:36:04

#=> 4/(y+3 )#

The denominator is the same...

#=> (4y-12)/(y^2-9) #

Factor #4y-12 -> 4(y-3) #

Use difference in two squares : #a^2 - b^2 = (a+b)(a-b) #

#=> y^2 - 9 -> (y+3)(y-3) #

#=> ( 4(y-3) ) / ( (y+3)(y-3) ) #

Cancel:

#=> ( 4cancel((y-3)) ) / ( (y+3)cancel((y-3)) ) #

#=> 4/(y+3 )#