`(3x)/(x - 3)^2` Write the partial fraction decomposition of the rational expression. Check your result algebraically.

`(3x)/(x-3)^2`

Let`(3x)/(x-3)^2=A/(x-3)+B/(x-3)^2`

`(3x)/(x-3)^2=(A(x-3)+B)/(x-3)^2`

`:.3x=A(x-3)+B`

`3x=Ax-3A+B`

equating the coefficients of the like terms,

`A=3`

`-3A+B=0`

plug the value of the A in the above equation,

`-3(3)+B=0`

`-9+B=0`

`B=9`

`:.(3x)/(x-3)^2=3/(x-3)+9/(x-3)^2`

`(3x)/(x-3)^2`

Let`(3x)/(x-3)^2=A/(x-3)+B/(x-3)^2`

`(3x)/(x-3)^2=(A(x-3)+B)/(x-3)^2`

`:.3x=A(x-3)+B`

`3x=Ax-3A+B`

equating the coefficients of the like terms,

`A=3`

`-3A+B=0`

plug the value of the A in the above equation,

`-3(3)+B=0`

`-9+B=0`

`B=9`

`:.(3x)/(x-3)^2=3/(x-3)+9/(x-3)^2`