How do you combine (3x-2)*[x/(3x^2+x-2)+2/(x+1)]?

1 Answer
Oct 1, 2016

(3x-2)*[x/(3x^2+x-2)+2/(x+1)]=(7x-4)/(x+1)

Explanation:

Let us first factorize 3x^2+x-2

3x^2+x-2=3x^2+3x-2x-2

= 3x(x+1)-2(x+1)

= (3x-2)(x+1)

Hence (3x-2)*[x/(3x^2+x-2)+2/(x+1)]

= (3x-2)*[x/((3x-2)(x+1))+2/(x+1)]

= (3x-2)xx x/((3x-2)(x+1))+(3x-2)xx2/(x+1)

= cancel(3x-2)xx x/(cancel((3x-2))(x+1))+(2(3x-2))/(x+1)

= x/(x+1)+(2(3x-2))/(x+1)

= (x+2(3x-2))/(x+1)

= (x+6x-4)/(x+1)

= (7x-4)/(x+1)