simplifying

[spacewater]

problem
\(\displaystyle \frac{(x+h)^2-x^2}{h}\)

\(\displaystyle \frac{(x+h)(x+h)-x^2}{h}\)
What more can I do from here?

 

[DrMike]

You could multiply out the brackets to get \(\displaystyle (x^2+2xh+h^2)\)

Can you see what to do after that?

 

[Aladdin]

\(\displaystyle \frac{(x+h)^2-x^2}{h}\)

a^2 - b^2 = (a-b)(a+b)

\(\displaystyle \frac{(x+h-x)(x+h+x)}{h}\)

\(\displaystyle \frac{(h)(2x+h)}{h}\)

Complete ...