Hey everyone I need some help with this problem that I have. I know that I put partial fractions into the title but I am unsure if that is truly what I need in order to complete this question. All my instructions says is:

Solve the following integral

This is it:

$\displaystyle \int\frac{{x}}{{(x-1)}{(\sqrt{x}-1)}}dx$

This is my method to solve:

$\displaystyle \int\frac{{x}}{{(x-1)}{(\sqrt{x}-1)}}dx = \frac{A}{x-1}+\frac{B}{\sqrt{x}-1}$

I multiplied both sides by the denominator of the left side:

$\displaystyle \int{x}dx = A(\sqrt{x}-1) + B(x-1)$

I factor in the A and B:

$\displaystyle x = A\sqrt{x} - A + Bx - B$

but this is where I am stuck at.. I mean the square root is where I am stuck at because the right and left sides aren't like terms right? Could definitely use some help with this one.

Thanks in advance