Advertisements
Advertisements
Question
Resolve into partial fraction for the following:
`(4x + 1)/((x - 2)(x + 1))`
Solution
Let `(4x + 1)/((x - 2)(x + 1)) = "A"/(x - 2) + "B"/(x + 1)` .....(1)
Multiply both sides by (x – 2) (x + 1) we get
4x + 1 = A(x + 1) + B(x – 2) ……. (2)
Put x = -1 in (2) we get
4(-1) + 1 = A(-1 + 1) + B(-1 – 2)
-4 + 1 = A(0) + B(-3)
-3 = B(-3)
B = `(-3)/(-3)` = 1
Put x = 2 in (2) we get
4(2) + 1 = A(2 + 1) + B(2 – 2)
8 + 1 = A(3) + B(0)
9 = 3A
A = 3
Using A = 3, B = 1 in (1) we get
`(4x + 1)/((x - 2)(x + 1)) = 3/(x - 2) + 1/(x + 1)`
APPEARS IN
RELATED QUESTIONS
Resolve into partial fraction for the following:
`(3x + 7)/(x^2 - 3x + 2)`
Resolve into partial fraction for the following:
`(x - 2)/((x + 2)(x - 1)^2)`
Resolve into partial fraction for the following:
`(2x^2 - 5x - 7)/(x - 2)^3`
Resolve into partial fraction for the following:
`(x^2 - 3)/((x + 2)(x^2 + 1))`
Resolve into a partial fraction for the following:
`(x + 2)/((x - 1)(x + 3)^2)`
Resolve into a partial fraction for the following:
`1/((x^2 + 4)(x + 1))`
Resolve into Partial Fractions:
`(5x + 7)/((x-1)(x+3))`
Decompose into Partial Fractions:
`(6x^2 - 14x - 27)/((x + 2)(x - 3)^2)`
Decompose into Partial Fractions:
`(5x^2 - 8x + 5)/((x - 2)(x^2 - x + 1))`
If `(kx)/((x + 4)(2x - 1)) = 4/(x + 4) + 1/(2x - 1)` then k is equal to:
