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# P3 Partial Qs HELP! watch

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1. express as partial fractions :

1) 4x^4+6x^3+4x^2+x-3/x^2(2x+3)

2) X^2+2x+3/x^2(x+1)

thank you!
2. 1)
4x^4+6x^3+4x^2+x-3/x^2(2x+3) = 2x + 2/x - [5x + 3]/[x²(2x + 3)]

[5x + 3]/[x²(2x + 3)] = (Ax + B)/x² + C/(2x + 3)
(5x + 3) = (Ax + B)(2x + 3) + Cx²
(5x + 3) = 2Ax² + (3A + 2B)x + 3B + Cx²
(5x + 3) = = (2A + C)x² + (3A + 2B)x + 3B

comparing coefficents,

0 = (2A + C)
5 = (3A + 2B)
3 = 3B

giving,

A = 1, B = 1, C = -2
===============

Expr = 2x + 2/x - (x + 1)/x² + 2/(2x + 3)
Expr = 2(x² + 1)/x - (x + 1)/x² + 2/(2x + 3)
================================ =

2)
X^2+2x+3/x^2(x+1) = (Ax + B)/x² + C/(x + 1)
X^2+2x+3 = (Ax + B)(x + 1) + Cx²
X^2+2x+3 = Ax² + (A + B)x + B + Cx²
X^2+2x+3 = (A + C)x² + (A + B)x + B

comparing coefficients,

1 = (A + C)
2 = (A + B)
3 = B

giving,

A = -1, B = 3, C = 2
===============

Expr = (-x + 3)/x² + 2/(x + 1)
======================
3. (Original post by Fermat)
1)
4x^4+6x^3+4x^2+x-3/x^2(2x+3) = 2x + 2/x - [5x + 3]/[x²(2x + 3)]

[5x + 3]/[x²(2x + 3)] = (Ax + B)/x² + C/(2x + 3)
(5x + 3) = (Ax + B)(2x + 3) + Cx²
(5x + 3) = 2Ax² + (3A + 2B)x + 3B + Cx²
(5x + 3) = = (2A + C)x² + (3A + 2B)x + 3B

comparing coefficents,

0 = (2A + C)
5 = (3A + 2B)
3 = 3B

giving,

A = 1, B = 1, C = -2
===============

Expr = 2x + 2/x - (x + 1)/x² + 2/(2x + 3)
Expr = 2(x² + 1)/x - (x + 1)/x² + 2/(2x + 3)
================================ =

2)
X^2+2x+3/x^2(x+1) = (Ax + B)/x² + C/(x + 1)
X^2+2x+3 = (Ax + B)(x + 1) + Cx²
X^2+2x+3 = Ax² + (A + B)x + B + Cx²
X^2+2x+3 = (A + C)x² + (A + B)x + B

comparing coefficients,

1 = (A + C)
2 = (A + B)
3 = B

giving,

A = -1, B = 3, C = 2
===============

Expr = (-x + 3)/x² + 2/(x + 1)
======================
fermat u r da man!

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