Advertisements
Advertisements
Question
Resolve the following rational expressions into partial fractions
`(3x + 1)/((x - 2)(x + 1))`
Solution
`(3x + 1)/((x - 2)(x + 1)) = "A"/(x - 2) + "B"/(x + 1)`
`(3x + 1)/((x - 2)(x + 1)) = ("A"(x + 1) + "B"(x - 2))/((x - 2)(x + 1))`
3x + 1 = A(x + 1) + B(x – 2) ......(1)
Put x = 2 in equation (1)
3(2) + 1 = A(2 + 1) + B(2 – 2)
6 + 1 = 3A + 0
⇒ A = `7/3`
Put x = – 1 in equation (1)
3(– 1) + 1 = A(– 1 + 1) + B(– 1 – 2)
– 3 + 1 = A × 0 – 3B
– 2 = 0 – 3B
⇒ B = `2/3`
∴ The required partial fractions are
`(3x + 1)/((x - 2)(x + 1)) = (7/3)/(x - 2) + (2/3)/(x + 1)`
`(3x + 1)/((x - 2)(x + 1)) = 7/(3(x - 2)) + 2/(3(x + 1))`
APPEARS IN
RELATED QUESTIONS
Find all values of x for which `(x^3(x - 1))/((x - 2)) > 0`
Find all values of x that satisfies the inequality `(2x - 3)/((x - 2)(x - 4)) < 0`
Solve `(x^2 - 4)/(x^2 - 2x - 15) ≤ 0`
Resolve the following rational expressions into partial fractions
`x/((x - 1)^3`
Resolve the following rational expressions into partial fractions
`(x^2 + x + 1)/(x^2 - 5x + 6)`
Resolve the following rational expressions into partial fractions
`(x^3 + 2x + 1)/(x^2 + 5x + 6)`
Resolve the following rational expressions into partial fractions
`(6x^2 - x + 1)/(x^3 + x^2 + x + 1)`
Resolve the following rational expressions into partial fractions
`(2x^2 + 5x - 11)/(x^2 + 2x - 3)`
Resolve the following rational expressions into partial fractions
`(7 + x)/((1 + x)(1 + x^2))`
Determine the region in the plane determined by the inequalities:
x ≤ 3y, x ≥ y
Determine the region in the plane determined by the inequalities:
y ≥ 2x, −2x + 3y ≤ 6
Determine the region in the plane determined by the inequalities:
3x + 5y ≥ 45, x ≥ 0, y ≥ 0
Determine the region in the plane determined by the inequalities:
2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0
Determine the region in the plane determined by the inequalities:
2x + y ≥ 8, x + 2y ≥ 8, x + y ≤ 6
Choose the correct alternative:
The solution of 5x − 1 < 24 and 5x + 1 > −24 is
Choose the correct alternative:
The solution set of the following inequality |x − 1| ≥ |x − 3| is
