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

jmc

algebra intermediate

Problem

Solve

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

for

x

Solution

Cross-multiplication gives

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

Therefore

0 = 2 x + 1

and

x = - \frac{1}{2}

Final answer

-\frac12