Steps to Simplify

Question

I am struggling to see how the following problem is simplified. Can someone include any steps that may have been skipped?

Original Equation= $\frac{T(p-b)}{(p-b+q-a)}$

Simplified Equation= $T\times\frac1{1+\frac{(q-a)}{p-b})}$

Answer 1

Dividing top and bottom by $p-b$ gives

$$\dfrac{p-b}{p-b+q-a}=\dfrac{\dfrac{p-b}{p-b}}{\dfrac{p-b+q-a}{p-b}}=\dfrac{1}{\dfrac{p-b}{p-b}+\dfrac{q-a}{p-b}}=\dfrac{1}{1+\dfrac{q-a}{p-b}}$$

Answer 2

You have $$ (p-b+q-a)=((p-b)+(q-a))=(p-b)\times\left( 1+\frac{q-a}{p-b}\right) $$ thus, simplifying by $\color{red}{(p-b)} \neq 0$, gives $$ \frac{T(p-b)}{(p-b+q-a)}=\frac{\color{red}{(p-b)}\times T }{\color{red}{(p-b)}\times\left( 1+\frac{q-a}{p-b}\right)}=\frac{T}{ 1+\frac{q-a}{p-b}}. $$