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

We want to solve

moving -3/x to the other side we have

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

Continuing we have

`\begin{gathered} (x+5)/(x^2-x)=(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=(8)/(3) \end{gathered}`

Hence the answer is 8/3