$$\frac{1}{q+1} = \frac{q}{3q-1}$$
Answer
$$ q = 1 $$
Explanation
$$ \begin{aligned} \frac{1}{q+1} &= \frac{q}{3q-1}&& \text{multiply ALL terms by } \color{blue}{ (q+1)(3q-1) }. \\[1 em](q+1)(3q-1)\cdot\frac{1}{q+1} &= (q+1)(3q-1)\frac{q}{3q-1}&& \text{cancel out the denominators} \\[1 em]3q-1 &= q^2+q&& \text{move all terms to the left hand side } \\[1 em]3q-1-q^2-q &= 0&& \text{simplify left side} \\[1 em]-q^2+2q-1 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+2x-1 = 0 $ is a quadratic equation.
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