Answered By Arko G

P(x)/(x-a)= (Q(x)(x-a)+R)/(x-a)

multiplying by (x-a) on both sides,

P(x)=Q(x)(x-a)+R; a not equal to 0

Answered By Chirag K

multiplying both sides by (  $x-a$x−a )

the equation becomes 

 $\frac{P\left(x\right)}{\left(x-a\right)}\left(x-a\right)=Q\left(x\right)\left(x-a\right)+\frac{R}{\left(x-a\right)}\left(x-a\right)$P(x)(x−a) (x−a)=Q(x)(x−a)+R(x−a) (x−a) 

since  $\frac{\left(x-a\right)}{\left(x-a\right)}=1$(x−a)(x−a) =1 

so the result is

 $P\left(x\right)=Q\left(x\right)\left(x-a\right)+R$P(x)=Q(x)(x−a)+R 

Note: the result is true iff  $x\ne a$x≠a otherwise we will me multiplying the equation by 0.