Alberta Free Tutoring And Homework Help For Math 30-1

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Show that P(x)/x-a = Q(x)+ R/x-a can be rearranged to P(x)= Q(x)(x-a)+R

4 years ago

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


4 years ago

Answered By Chirag K

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

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)(xa) (xa)=Q(x)(xa)+R(xa) (xa) 

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

so the result is

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

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