Simplify expression

**CantcountWontcount** · October 2nd 2009, 10:49 AM

Any help would be appreciated... thanks

a2b
__________
ab2 – a1/2 b3

**gs.sh11** · October 2nd 2009, 10:56 AM

a2b
__________
ab2 – a1/2 b3 -- Is a2b $a^2b$ or just a(2b)? - Please use paranthesis and ^ signs for exponents, so it is easier to read.

**e^(i*pi)** · October 2nd 2009, 10:57 AM

Originally Posted by Mr Smith

please use latex, I can't understand your problem.

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

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

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

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

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

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

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

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

And you may cancel a $b$

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

**CantcountWontcount** · October 2nd 2009, 11:02 AM

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

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