32 Partial fraction decomposition; Question 32.8

[Eigenvalue]

32.8. Find the partial fraction decomposition of [tex]\frac{11x-10}{x²-2x}[/tex]

[Eigenvalue]

a) As the numerator has a lower degree than the diameter, there is no need to use polynomial long division
Note: if the degree of he numerator is higher than that of the denominator, first use polynomial long division to simplify.

b) Rewrite [tex]\frac{11x-10}{x²-2x}[/tex] as [tex]\frac{A}{x}[/tex]+[tex]\frac{B}{x-2}[/tex]

[tex]\frac{11x-10}{x²-2x}[/tex]=[tex]\frac{A(x-2)+Bx}{x(x-2)}[/tex]

c) The denominator for both fractions are equal, therefore, the numerator is also equal
11x-10=A(x-2)+Bx

d) Solve for A and B
11x-10=Ax+Bx-2A
-2A=-10
A=5
A+B=11
B=6

e)[tex]\frac{11x-10}{x²-2x}[/tex]=[tex]\frac{5}{x}[/tex]+[tex]\frac{6}{x-2}[/tex]