Simplify fraction $4x/(x-1)$ to $ 4+(4/(x-1))$

Question

I have put the fraction into Symbolab which gives some step-by-step explanation on why this os correct, but I am unable to grasp how this is possible.

Answer 1

Adding and $+4$ and $-4$ to the numerator, if $x\in \Bbb R \setminus \{1\}$, you have:

$$\frac{4x}{x-1}=\frac{(4x-4)+4}{x-1}=\frac{4x-4}{x-1}+\frac4{x-1}=4\frac{x-1}{x-1}+\frac4{x-1}=4+\frac4{x-1}$$