SOLUTION: Decompose into partial fractions (check your answers)[x^2 -10x +13]/[x^2 -5x +6)(x-1)]

Question 61310This question is from textbook College Algebra Graphs and Models
: Decompose into partial fractions (check your answers)[x^2 -10x +13]/[x^2 -5x +6)(x-1)] This question is from textbook College Algebra Graphs and Models

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Decompose into partial fractions (check your answers)[x^2 -10x +13]/[x^2 -5x +6)(x-1)]
=[X^2-10X+13]/[(X-2)(X-3)(X-1)]
= A/(X-1) + B/(X-2) + C/(X-3)
X^2-10X+13 = A(X-2)(X-3) +B(X-1)(X-3) +C(X-1)(X-2)
PUTTING X=1,2 AND 3 IN ORDER , WE GET...
A =[1-10+13]/[(1-2)(1-3)= 4/2=2
B= [4-20+13]/(2-1)(2-3)=-3/-1=3
C=[9-30+13]/(3-1)(3-2)=-8/2 = -4
HENCE ANSWER IS
2/(X-1) +3/(X-2) - 4/(X-3)...I HOPE YOU CAN CHECK BY MULTIPLICATION.
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