How do you simplify #\frac { ( 4- \frac { 12} { 2x - 3} ) } { ( 5+ \frac { 15} { 2x - 3} ) }#?

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Answer 1 · 2017-07-24T22:32:46

#4/5#

Combine the addition and subtraction of fractions into single fractions by finding a common denominator.

#(4/1-12/(2x-3))div(5/1+15/(2x-3))#

#=((4(2x-3)-12)/(2x-3))div ((5(2x-3)+15)/(2x-3))#

#=((8x-12-12)/(2x-3))div((10x-15-15)/(2x-3))#

Simplify and then to divide, multiply by the reciprocal.

#=((8x-24)/(2x-3))xx((2x-3)/(10x-30))#

Factorise and simplify

#=(8cancel((x-3)))/cancel((2x-3)) xx cancel((2x-3))/(10cancel((x-3))#

#=8/10#

#=4/5#