Question

Solve
4-p/p-1=2/p-1

Answer 1

Final answer is p=2.

Explanation:

Given equation is
`(4-p)/(p-1)=(2)/(p-1)`

Cross multiply

`\left(4-p\right)\left(p-1\right)=2\left(p-1\right)`

`4p-4-p^2+p=2p-2`

`4p-4-p^2+p=2p-2`

`0=p^2-4p+4-p+2p-2`

`0=p^2-3p+2`

`0=p^2-1p-2p+2`

`0=(p-1)(p-2)`

`0=(p-1)` or
`0=(p-2)`

`1=p` or
`2=p`

But p=1 will make denominator 0 and make the problem not defined.

Hence final answer is p=2