(2/x^2)-(2/x+10)=1/x-1

(2/x^2)-(2/x+10)=1/x-1

Omi67 

is it possible to multiply both sides with variable ? i.e ${x}^{2}$

Thanks Omi,  

Hi 315, Let's see what I would do.

Now that I have already done it all I can see that Omi DID multiply by x^2

Our solutions are almot identical.  

(2/x^2)-(2/x+10)=1/x-1

$\begin{align}\\ \frac{2}{x^2}-(\frac{2}{x}+10)&=\frac{1}{x}-1\qquad {x\ne0}\\ \frac{2}{x^2}-\frac{2}{x}-10&=\frac{1}{x}-1\\ \frac{2}{x^2}-\frac{3}{x}-9&=0\\ x^2\left(\frac{2}{x^2}-\frac{3}{x}-9\right)&=x^2*0\\~\\ 2-3x-9x^2&=0\\ 9x^2+3x-2&=0\\ x&=\frac{-3\pm\sqrt{9+72}}{18}\\ x&=\frac{-3\pm9}{18}\\ x&=\frac{-1\pm3}{6}\\ \end{align}\\~\\ x=\dfrac{-2}{3}\qquad or \qquad x=\dfrac{1}{3}$