Question

Please help me with this, I don’t understand anything and all the tutors are making it so difficult, please make it simple and easy, thank you!

Answer 1

SOLUTION

We want to solve

moving -3/x to the other side we have

$\begin{gathered} \frac{x+5}{x^2-x}=\frac{1}{x-1}+\frac{3}{x} \\ adding\text{ the other side by LCM, we have } \\ \frac{x+5}{x^2-x}=\frac{x+3(x-1)}{(x-1)x} \\ expanding\text{ we have } \\ \frac{x+5}{x^2-x}=\frac{x+3x-3}{x^2-x} \\ \frac{x+5}{x^2-x}=\frac{4x-3}{x^2-x} \end{gathered}$

Continuing we have

$\begin{gathered} \frac{x+5}{x^2-x}=\frac{4x-3}{x^2-x} \\ cancelling\text{ common denominators, we have } \\ x+5=4x-3 \\ collecting\text{ like terms } \\ 5+3=4x-x \\ 8=3x \\ x=\frac{8}{3} \end{gathered}$

Hence the answer is 8/3