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.

I suggest that you transcribe the step-by-step explanation you have, and then explain how much you understand and where you get stuck or confused. — halrankard, Jul 13 '20 at 15:04

score 3 · Accepted Answer · answered Jul 13 '20 at 15:06

3

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

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

answered Jul 13 '20 at 15:06

Sebastiano

7,649

1

Thanks, this is exactly what I am looking for. Totally forgot you could add and substract like that. – Gertjan Brouwer Jul 13 '20 at 15:14
@GertjanBrouwer There's no problem with me. In fact, it is a sincere pleasure. Do you know how much I forget? Many many. :-) – Sebastiano Jul 13 '20 at 15:16
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Good to hear I am not the only one forgetting things! – Gertjan Brouwer Jul 13 '20 at 15:18
@GertjanBrouwer I always put humility and sincerity first, but this bothers a lot of people. – Sebastiano Jul 13 '20 at 15:19
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Well I really do appreciate it, thanks again – Gertjan Brouwer Jul 13 '20 at 15:29

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

1 Answers1