Number of Partial Fractions of 2x-3-x2x2-13

The correct option is C 8 2x+3/x^2(x^2 1)^3=2x+3/x^2(x+1)^3(x 1)^3 2x+3/x^2(x+1)^3(x 1)^3=A/x+B/x^2+C/(x+1)+D/(x+1)^2+E/(x+1)^3 +F/(x 1)+G/(x 1)^2 ...

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Byju's Answer

Standard XII

Mathematics

Functions

Number of Par...

Question

Number of Partial Fractions of $\frac{2 x + 3}{x^{2} (x^{2} - 1)^{3}}$

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Solution

The correct option is C 8
$\frac{2 x + 3}{x^{2} (x^{2} - 1)^{3}} = \frac{2 x + 3}{x^{2} (x + 1)^{3} (x - 1)^{3}}$
$\frac{2 x + 3}{x^{2} (x + 1)^{3} (x - 1)^{3}} = \frac{A}{x} + \frac{B}{x^{2}} + \frac{C}{(x + 1)} + \frac{D}{(x + 1)^{2}} + \frac{E}{(x + 1)^{3}}$
$+ \frac{F}{(x - 1)} + \frac{G}{(x - 1)^{2}} + \frac{H}{(x - 1)^{3}}$
So, these are 8 partial fractions.

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Number of Partial Fractions of 2x+3x2(x2−1)3

The correct option is C 82x+3x2(x2−1)3=2x+3x2(x+1)3(x−1)32x+3x2(x+1)3(x−1)3=Ax+Bx2+C(x+1)+D(x+1)2+E(x+1)3+F(x−1)+G(x−1)2+H(x−1)3So, these are 8 partial fractions.

Number of Partial Fractions of $\frac{2 x + 3}{x^{2} (x^{2} - 1)^{3}}$