Solve M=(frac{x+sqrt{x}+10}{x-9}-1/sqrt{x-3}):1/sqrt{x-3}

$$M = ( \frac { x + \sqrt { x } + 10 } { x - 9 } - \frac { 1 } { \sqrt { x } - 3 } ) : \frac { 1 } { \sqrt { x } - 3 }$$

Solve for M (complex solution)

$$M=\frac{x+7}{\sqrt{x}+3}$$

$$x\neq 9$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\left(\sqrt{\left(M-2\right)\left(M+14\right)}+M\right)^{2}}{4}\text{, }&M\neq \frac{8}{3}\text{ and }arg(\frac{\sqrt{\left(M-2\right)\left(M+14\right)}+M}{2})<\pi \\x=\frac{\left(-\sqrt{\left(M-2\right)\left(M+14\right)}+M\right)^{2}}{4}\text{, }&M=\frac{7}{3}\text{ or }arg(\frac{-\sqrt{\left(M-2\right)\left(M+14\right)}+M}{2})<\pi \end{matrix}\right.$$

Solve for M

$$M=\frac{x+7}{\sqrt{x}+3}$$

$$x\geq 0\text{ and }x\neq 9$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\left(\sqrt{\left(M-2\right)\left(M+14\right)}+M\right)^{2}}{4}\text{, }&\frac{\sqrt{\left(M-2\right)\left(M+14\right)}+M}{2}\geq 0\text{ and }\left(M\leq -14\text{ or }M\geq 2\right)\text{ and }M\neq \frac{8}{3}\\x=\frac{\left(-\sqrt{\left(M-2\right)\left(M+14\right)}+M\right)^{2}}{4}\text{, }&\left(M\leq -14\text{ or }M\geq 2\right)\text{ and }\frac{-\sqrt{\left(M-2\right)\left(M+14\right)}+M}{2}\geq 0\end{matrix}\right.$$