# How do you solve for y in x=(y+2)/(5y-1)?

Jun 19, 2016

color(blue)(y = (2 + x) / (5x - 1)

#### Explanation:

$x = \frac{\textcolor{b l u e}{y} + 2}{5 \textcolor{b l u e}{y} - 1}$

Our main motive in solving this question should be to isolate color(blue)(y:

$x \cdot \left(5 \textcolor{b l u e}{y} - 1\right) = \textcolor{b l u e}{y} + 2$

We multiply $x$ with both terms within the bracket.

$x \cdot \left(5 \textcolor{b l u e}{y}\right) + x \cdot \left(- 1\right) = \textcolor{b l u e}{y} + 2$

$5 x \textcolor{b l u e}{y} - x = \textcolor{b l u e}{y} + 2$

$5 x \textcolor{b l u e}{y} - \textcolor{b l u e}{y} = 2 + x$

$\textcolor{b l u e}{y} \left(5 x - 1\right) = 2 + x$

color(blue)(y = (2 + x) / (5x - 1)