# How do you solve (x-1)/(7x+6)=2/(x+2) and check for extraneous solutions?

Oct 24, 2016

Use the property $\frac{a}{b} = \frac{c}{d} \to a \times d = b \times c$ to start the solving process.

$\left(x - 1\right) \left(x + 2\right) = 2 \left(7 x + 6\right)$

${x}^{2} - x + 2 x - 2 = 14 x + 12$

${x}^{2} + x - 2 = 14 x + 12$

${x}^{2} - 13 x - 14 = 0$

$\left(x - 14\right) \left(x + 1\right) = 0$

$x = 14 \mathmr{and} - 1$

None of these solutions are extraneous, since they do not go against the initial restrictions of $- \frac{6}{7}$ and $- 2$.

Hopefully this helps!