Advertisements
Advertisements
प्रश्न
Resolve the following rational expressions into partial fractions
`1/(x^2 - "a"^2)`
उत्तर
`1/(x^2 - "a"^2) = 1/((x + "a")(x - "a"))`
`1/(x^2 - "a"^2) = "A"/(x + "a") + "B"/(x - "a")`
`1/(x^2 - "a"^2) = ("A"(x - "a") + "B"(x + "a"))/((x + "a")(x - "a"))`
1 = A(x – a) + B(x + a) ......(1)
Put x = a in equation (1)
1 = A(0) + B(a + a)
1 = B(2a)
⇒ B = `1/(2"a")`
Put x = – a in equation (1)
1 = A(– a – a) + B(– a + a)
1 = – 2a A + 0
⇒ A = `- 1/(2"a")`
∴ The required partial fraction is
`1/(x^2 - "a"^2) = (-1/(2"a"))/(x + "a") + (1/(2"a"))/(x -- "a")`
`1/(x^2 - "a"^2) = 1/(2"a"(x - "a")) - 1/(2"a"(x + "a"))`
APPEARS IN
संबंधित प्रश्न
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
`(3x + 1)/((x - 2)(x + 1))`
Resolve the following rational expressions into partial fractions
`x/((x^2 + 1)(x - 1)(x + 2))`
Resolve the following rational expressions into partial fractions
`1/(x^4 - 1)`
Resolve the following rational expressions into partial fractions
`(x - 1)^2/(x^3 + x)`
Resolve the following rational expressions into partial fractions
`(x + 12)/((x + 1)^2 (x - 2))`
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:
3x + 5y ≥ 45, x ≥ 0, y ≥ 0
Determine the region in the plane determined by the inequalities:
2x + 3y ≤ 35, y ≥ 2, x ≥ 5.
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
