College Algebra, Chapter 1, 1.1, Section 1.1, Problem 44

The equation $\displaystyle \frac{1}{1- \frac{3}{2+w}} = 60$ is either linear or equivalent to a linear equation. Solve the equation

$\begin{equation} \begin{aligned} \frac{1}{1- \frac{3}{2+w}} &= 60 && \text{Get the LCD}\\ \\ \frac{1}{\frac{2+w-3}{2+w}} &= 60 && \text{Combine like terms}\\ \\ \frac{1}{\frac{w-1}{w+2}} &= 60 && \text{Get the reciprocal}\\ \\ \frac{w+2}{w-1} &= 60 && \text{Multiply both sides by }(w-1)\\ \\ \cancel{(w-1)} & \left[ \frac{w+2}{\cancel{w-1}} = 60 \right] (w-1) && \text{Cancel out like terms}\\ \\ w +2 &= 60 (w-1) && \text{Simplify}\\ \\ w +2 &= 60w - 60 && \text{Combine like terms}\\ \\ w - 60w &= -2 - 60 && \text{Simplify}\\ \\ -59w &= -62 && \text{Divide both sides by -59}\\ \\ \frac{\cancel{-59}w}{\cancel{-59}} &= \frac{-62}{-59} && \text{Cancel Out like terms}\\ \\ w &= \frac{62}{59} \end{aligned} \end{equation}$