How do you simplify #\frac { 5- \frac { 5a } { a - 1} } { 2- \frac { 5a + 1} { 3a } }#?

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Answer 1 · 2016-11-20T15:50:36

#(-15a)/(a-1)^2#

#[5-frac{5a}{a-1}]/[2-frac{5a+1}{3a}]#

Make there be only one term on the top, and one term on the bottom. Use common denominators:
#=frac{5(a-1)-5a}{a-1}/frac{2(3a)-(5a+1)}{3a}#

Simplify:
#=((frac{5a-5-5a}{a-1}))/((frac{6a-5a-1}{3a}))#

#=((frac{-5}{a-1}))/((frac{a-1}{3a}))#

Rewrite division as multiplying by the reciprocal:
#=((-5)/(a-1))((3a)/(a-1))#

Multiply:

#=(-15a)/(a-1)^2#