Simplifying this radical expression?

Question

We are given:

$ f(x) = √x - 2e^x$

and we have to calculate the difference quotient ($\frac{f(x+h)-f(x)}{h})$

So what I have so far is:

$ \frac{√(x+h)-2e^{(x+h)} - (√x - 2e^x)}{h} $

I would assume you would multiply the numerator by the conjugate correct?:

($ {√(x+h)+2e^{(x+h)} + (√x + 2e^x))} $

Answer 1

$\frac{√(x+h)-2e^{(x+h)} - (√x - 2e^x)}{h}=\frac{\sqrt{x+h}-\sqrt{x}}{h}-2\frac{e^{x+h}-e^{x}}{h}$ by multiplying the numerator and denominator of the first term with $\sqrt{x+h}+\sqrt{x}$, we have $\frac{1}{\sqrt{x+h}+\sqrt{x}}-2e^{x}\frac{e^{h}-1}{h}$