Answer:
Final answer is p=2.
Step-by-step explanation:
Given equation is [tex]\frac{4-p}{p-1}=\frac{2}{p-1}[/tex]
Cross multiply
[tex]\left(4-p\right)\left(p-1\right)=2\left(p-1\right)[/tex]
[tex]4p-4-p^2+p=2p-2[/tex]
[tex]4p-4-p^2+p=2p-2[/tex]
[tex]0=p^2-4p+4-p+2p-2[/tex]
[tex]0=p^2-3p+2[/tex]
[tex]0=p^2-1p-2p+2[/tex]
[tex]0=(p-1)(p-2)[/tex]
[tex]0=(p-1)[/tex] or [tex]0=(p-2)[/tex]
[tex]1=p[/tex] or [tex]2=p[/tex]
But p=1 will make denominator 0 and make the problem not defined.
Hence final answer is p=2
