Solve 3x^2+2x+1x-1=3x+1for x.

jmc

algebra intermediate

Problem

Solve

\frac{3 x ^{2} + 2 x + 1}{x - 1} = 3 x + 1

for

x

Solution

Cross-multiplication gives

3 x^{2} + 2 x + 1 = (x - 1) (3 x + 1) = 3 x^{2} - 2 x - 1.

Therefore

4 x = - 2

and

x = - \frac{1}{2}

Final answer

-\frac{1}2