Partial Fractions

Question 1

13/(5+x)(3-2x)=

Answer 1

A/(5+x) + B/(3-2x)

A(3-2x) + B(5+x)=13

x=3/2, A=0, 6.5B=13, B=2

x=-5, B=0, 13A=13, A=1

1/(5+x) +2/(3-2x)

Question 2

3x-4/(2x-1)(x+2)(x-3) =

Answer 2

(2/5/2x-1) + (-2/5/x+2) + (1/5/x-3)

2/5(2x-1) - 2/5(x+2) + 1/5(x-3)

Question 3

2x²+3x-1/x²-1 =

Answer 3

2 + 3x+1/x²-1

=2+3x+1/(x-1)(x+1)

2+ (2/x-1) + 1/x+1

Question 4

x-8/(x+1)(x-2)²

Answer 4

write as a partial fraction

A/(x+1) + B(x-2) + C/(x-2)2

x-8=A(x-2)2 +B(x+1)(x-2) +C(x+1)

A=-1, C=-2 to find B do x=3, B=1

=-1/x+1 + 1/x-2 - 2/(x-2)2