Help Partial Fractions

**Cthul** · June 9th 2010, 12:29 AM

$\frac{1+x}{x(1+x^{2})}$

When I expand this, I can't eliminate to get one variable to get the variable.

**Prove It** · June 9th 2010, 12:37 AM

Originally Posted by Cthul

$\frac{1+x}{x(1+x^{2})}$

When I expand this, I can't eliminate to get one variable to get the variable.

Write it as

$\frac{A}{x} + \frac{Bx + C}{1 + x^2} = \frac{1 + x}{x(1 + x^2)}$

$\frac{A(1 + x^2) + (Bx + C)x}{x(1 + x^2)} = \frac{1 + x}{x(1 + x^2)}$

$A(1 + x^2) + (Bx + C)x = 1 + x$

$A + Ax^2 + Bx^2 + Cx = 1 + x$

$(A + B)x^2 + Cx + A = 0x^2 + x + 1$ .

Equating coefficients of like powers of $x$ gives

$A + B = 0, C = 1, A = 1$ .

So $B = -1$ .

Therefore:

$\frac{1}{x} + \frac{1 - x}{1 + x^2} = \frac{1 + x}{x(1 + x^2)}$ .

**Cthul** · June 9th 2010, 01:47 AM

Thank you, problem solved. I understand how now.

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