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by **vero23** » Thu Jul 29, 2010 8:02 pm

what is the solution to (3x)/(x-3)^2

please help

by **galactus** » Thu Jul 29, 2010 8:42 pm

$\frac{A}{x-3}+\frac{B}{(x-3)^{2}}=3x$

Multiply both sides of the decomposition by the LCD, $(x-3)^{2}$

$(x-3)^{2}\cdot \frac{A}{x-3}+\frac{B}{(x-3)^{2}}\cdot (x-3)^{2}=3x$

$A(x-3)+B=3x$

$Ax-3A+B=3x$

Equate coefficients:

$A=3$

$-3A+B=0$

Solve for A and B.

It is obvious that A=3 and B=9

$\frac{3}{x-3}+\frac{9}{(x-3)^{2}}$

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