# Simplify expression

• Oct 2nd 2009, 10:49 AM
CantcountWontcount
Simplify expression
Any help would be appreciated... thanks

a2b
__________
ab2 – a1/2 b3
• Oct 2nd 2009, 10:56 AM
gs.sh11
a2b
__________
ab2 – a1/2 b3 -- Is a2b $\displaystyle a^2b$ or just a(2b)? - Please use paranthesis and ^ signs for exponents, so it is easier to read.
• Oct 2nd 2009, 10:57 AM
e^(i*pi)
Quote:

Originally Posted by Mr Smith

I'd suspect $\displaystyle \frac{a^2b}{ab^2+b^3\sqrt{a}}$

As it happens you can factor $\displaystyle \sqrt{a}$ and $\displaystyle b^2$ from the denominator:

$\displaystyle \frac{a^2b}{b^2\sqrt{a}(\sqrt{a}+b)}$

$\displaystyle b$ and $\displaystyle \sqrt{a}$ cancel:

$\displaystyle \frac{\sqrt{a}}{b(\sqrt{a}+b)}$

You could then multiply by it's conjugate if you wanted to rationalise the denominator

$\displaystyle \frac{\sqrt{a}}{b(\sqrt{a}+b)} \cdot \frac{b(\sqrt{a}-b)}{b(\sqrt{a}-b)}$

$\displaystyle = \frac {b\sqrt{a}(\sqrt{a}-b)}{b^2(a-b^2)}$

And you may cancel a $\displaystyle b$

$\displaystyle = \frac {\sqrt{a}(\sqrt{a}-b)}{b(a-b^2)}$
• Oct 2nd 2009, 11:02 AM
CantcountWontcount
Sorry only a newbie but will look up how to use it, for now its:

a squared x b
divided by
a x b squared - a to the power of 1/2 x b cubed