Thread: simplify

Simplify the following expression:

$\displaystyle \frac{6v^2+6u^2+12uv}{3vx+3ux+4uw+4vw}$

there are four alphabets used, which are v, u ,x and w.

what i tried to do is

$\displaystyle \frac{6v^2+6u^2+12uv}{3vx+3ux+4uw+4vw}$
=$\displaystyle \frac{6v^2+6u(u+2v)}{(3x+4w)(v+u)}$

then...stuck...
i think it can be further simplified..........

any help is much appreciated....

Originally Posted by wintersoltice

Simplify the following expression:

$\displaystyle \frac{6v^2+6u^2+12uv}{3vx+3ux+4uw+4vw}$

what i tried to do is

$\displaystyle \frac{6v^2+6u^2+12uv}{3vx+3ux+4uw+4vw}$
=$\displaystyle \frac{6v^2+6u(u+2v)}{(3x+4w)(v+u)}$

then...stuck...
i think it can be further simplified..........

any help is much appreciated....

$\displaystyle \frac{6(v^2+2uv+u^2)}{(3vx+3ux)+(4uw+4vw)}$

$\displaystyle \frac{6(v+u)^2}{3x(v+u)+4w(v+u)}$

$\displaystyle \frac{6(v+u)^2}{(3x+4w)(v+u)}$

do u know what to do now ?

Originally Posted by mathaddict

$\displaystyle \frac{6(v^2+2uv+u^2)}{(3vx+3ux)+(4uw+4vw)}$

$\displaystyle \frac{6(v+u)^2}{3x(v+u)+4w(v+u)}$

$\displaystyle \frac{6(v+u)^2}{(3x+4w)(v+u)}$

do u know what to do now ?

i see....
so the final answer is

$\displaystyle \frac{6(v+u)}{(3x+4w)}$...

thanks