# How do you solve the rational equation #(3a-2)/(2a+2)=3/(a-1)#?

##### 1 Answer

Jan 7, 2016

Multiply both sides by

#a=-1/3# or#a=4#

#### Explanation:

Multiply both sides by

#(3a-2)(a-1) = 3(2a+2)#

That is:

#3a^2-5a+2 = 6a+6#

Subtract

#3a^2-11a-4 = 0#

Factor this by noticing that

So:

#0 = 3a^2-11a-4#

#= (3a^2-12a) + (a-4)#

#= 3a(a-4)+1(a-4)#

#= (3a+1)(a-4)#

Hence

It remains to check that when we multiplied both sides by

That's OK since