need help

[friendsofstcorn]

(1/√(3(x+h)) - 1/√(3x))/h.....help, I keep trying to solve and am striking out, tried this:

 

[tkhunny]

Looks rather like you're just making a mess. Why not try to simplify your life a bit.

First, incorporate that 'h' in the denominator right away. No need to maintain it as a giant, horrible complicated fraction.

 

[friendsofstcorn]

i get it to -1/√(3x^2(x+h)) + √(3x(x+h)^2)

but can't simplify denominator......suggestions....?

 

[mmm4444bot]

Your scan is not easy for me to read. Also, the right side of your image is cut-off.

It looks like you somehow first simplified:

\(\displaystyle \frac{1}{\sqrt{3(x+h)}} - \frac{1}{\sqrt{3x}}\)

to:

\(\displaystyle \frac{\sqrt{x} - \sqrt{x+h}}{\sqrt{3x(x+h)}}\).

I got the following result, instead:

\(\displaystyle \frac{\sqrt{3}[\sqrt{x} - \sqrt{x+h}]}{3\sqrt{x(x+h)}}\)

Your idea is good to multiply the numerator and denominator by the conjugate of the numerator.

Give it another try.