<s>[INST] Differentiate and simplify. $m(x) = \frac{x}{\sqrt{4x-3}}$ My work so far is:
\begin{align}
m'(x) &= \frac{(1)(\sqrt{4x-3})-(x)(1/2)(4x-3)^{-1/2}(4)}{(\sqrt{4x-3})^2} \\
&= \frac{\sqrt{4x-3} - 2x(4x-3)^{1/2}}{4x-3}
\end{align}
and now I'm stuck on how to simplify further
 [/INST] In the right hand side of your second line, you wrote

$(4x-3)^{1/2}$

Note the exponent here is incorrect: it should still be $(4x-3)^{-1/2}$.  Let's write it that way and try to proceed.
$$m'(x)=\frac{\sqrt{4x-3}-2x(4x-3)^{-1/2}}{4x-3}=\frac{\sqrt{4x-3}-\frac{2x}{\sqrt{4x-3}}}{4x-3}$$
Now, in the numerator, we can simplify via finding a common denominator:
$$\sqrt{4x-3}-\frac{2x}{\sqrt{4x-3}}=\frac{4x-3-2x}{\sqrt{4x-3}}=\frac{2x-3}{\sqrt{4x-3}}$$
Putting this back in the numerator, we get:
$$m'(x)=\frac{\frac{2x-3}{\sqrt{4x-3}}}{4x-3}=\frac{2x-3}{(4x-3)^{3/2}}$$
This is as simplified as it's likely expected to be.
</s>