Solve y=exp(x+5/x-2)

$$y = \exp ( \frac { x + 5 } { x - 2 } )$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-\frac{y\left(2-x\right)}{ex\left(x+5\right)}\text{, }&x\neq -5\text{ and }x\neq 0\text{ and }x\neq 2\\p\in \mathrm{C}\text{, }&\left(x=0\text{ or }x=-5\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2.

$$y\left(x-2\right)=exp\left(x+5\right)$$

Use the distributive property to multiply y by x-2.

$$yx-2y=exp\left(x+5\right)$$

Use the distributive property to multiply exp by x+5.

$$yx-2y=epx^{2}+5exp$$

Swap sides so that all variable terms are on the left hand side.

$$epx^{2}+5exp=yx-2y$$

Combine all terms containing p.

$$\left(ex^{2}+5ex\right)p=yx-2y$$

The equation is in standard form.

$$\left(ex^{2}+5ex\right)p=xy-2y$$

Divide both sides by 5xe+ex^{2}.

$$\frac{\left(ex^{2}+5ex\right)p}{ex^{2}+5ex}=\frac{y\left(x-2\right)}{ex^{2}+5ex}$$

Dividing by 5xe+ex^{2} undoes the multiplication by 5xe+ex^{2}.

$$p=\frac{y\left(x-2\right)}{ex^{2}+5ex}$$

Divide y\left(-2+x\right) by 5xe+ex^{2}.

$$p=\frac{y\left(x-2\right)}{ex\left(x+5\right)}$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{y\left(2-x\right)}{ex\left(x+5\right)}\text{, }&x\neq -5\text{ and }x\neq 0\text{ and }x\neq 2\\p\in \mathrm{R}\text{, }&\left(x=0\text{ or }x=-5\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2.

$$y\left(x-2\right)=exp\left(x+5\right)$$

Use the distributive property to multiply y by x-2.

$$yx-2y=exp\left(x+5\right)$$

Use the distributive property to multiply exp by x+5.

$$yx-2y=epx^{2}+5exp$$

Swap sides so that all variable terms are on the left hand side.

$$epx^{2}+5exp=yx-2y$$

Combine all terms containing p.

$$\left(ex^{2}+5ex\right)p=yx-2y$$

The equation is in standard form.

$$\left(ex^{2}+5ex\right)p=xy-2y$$

Divide both sides by 5xe+ex^{2}.

$$\frac{\left(ex^{2}+5ex\right)p}{ex^{2}+5ex}=\frac{y\left(x-2\right)}{ex^{2}+5ex}$$

Dividing by 5xe+ex^{2} undoes the multiplication by 5xe+ex^{2}.

$$p=\frac{y\left(x-2\right)}{ex^{2}+5ex}$$

Divide y\left(-2+x\right) by 5xe+ex^{2}.

$$p=\frac{y\left(x-2\right)}{ex\left(x+5\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{y^{2}-18epy+25\left(ep\right)^{2}}-5ep+y}{2ep}\text{; }x=\frac{-\sqrt{y^{2}-18epy+25\left(ep\right)^{2}}-5ep+y}{2ep}\text{, }&p\neq 0\\x\neq 2\text{, }&y=0\text{ and }p=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{y^{2}-18epy+25\left(ep\right)^{2}}-5ep+y}{2ep}\text{; }x=\frac{-\sqrt{y^{2}-18epy+25\left(ep\right)^{2}}-5ep+y}{2ep}\text{, }&p\neq 0\text{ and }\left(y\geq 2e\sqrt{14}|p|+9ep\text{ or }y\leq -2e\sqrt{14}|p|+9ep\right)\\x\neq 2\text{, }&y=0\text{ and }p=0\end{matrix}\right.$$