College Algebra, Chapter 1, 1.1, Section 1.1, Problem 30

The equation $\displaystyle \frac{2x-1}{x+2} = \frac{4}{5}$ is either linear or equivalent to a linear equation. Solve the equation

$\begin{equation} \begin{aligned} \frac{2x-1}{x+2} &= \frac{4}{5} && \text{Multiply both sides by } 5(x+2)\\ \\ 5 \cancel{(x+2)} & \left[ \frac{2x-1}{\cancel{x+2}} = \frac{4}{\cancel{5}} \right] \cancel{5}(x+2) && \text{Simplify}\\ \\ 5 (2x -1 ) &= 4(x+2) && \text{Apply Distributive property}\\ \\ 10x - 5 &= 4x + 8 && \text{Combine like terms}\\ \\ 10x - 4x &= 8 +5 && \text{Simplify}\\ \\ 6x &= 13 && \text{Divide both sides by 6}\\ \\ \frac{\cancel{6}x}{\cancel{6}} &= \frac{13}{6} && \text{Simplify}\\ \\ x &= \frac{13}{6} \end{aligned} \end{equation}$