1. ## Literal Equations help

Could you guys help me with this maths methods question?

x/(a-b)+2x(a+b)=1/a2-b2

Solve for x

2. ## Re: Literal Equations help

Originally Posted by Tehmo3
Could you guys help me with this maths methods question?

x/(a-b)+2x(a+b)=1/a2-b2

Solve for x
$\displaystyle \frac{x}{a-b}+2x(a+b)=\frac{1}{a^2-b^2}$

$\displaystyle x+2x(a+b)(a-b)=\frac{a-b}{(a-b)(a+b)}$

$\displaystyle x\left(1+2(a^2-b^2)\right)=\frac{1}{a+b}$

$\displaystyle x=\frac{1}{(a+b)\left(1+2(a^2-b^2)\right)}$

3. ## Re: Literal Equations help

A slightly different way: $\displaystyle \frac{x}{a-b}+ 2x(a- b)= x\left(\frac{1}{a- b}+ 2(a+ b)\right)= \frac{1}{a^2- b^2}= \frac{1}{(a- b)(a+ b)}$
Add the fractions on the left:
$\displaystyle x\left(\frac{1}{a- b}+ \frac{2(a+ b)(a- b)}{a- b}\right)= x\left(\frac{1+ 2(a^2- b^2)}{a- b}\right)= \frac{1}{(a- b)(a+ b)}$

Divide both sides by the fraction multiplying x:
$\displaystyle x= \frac{1}{(a- b)(a+ b)}\frac{a- b}{1+ 2(a^2- b^2)}= \frac{1}{(a+ b)(1+ 2(a^2- b^2))}$
because the two "a- b" factor cancel.