Solve U=exp(2/x^3-3/x^2)

$$U = \exp ( \frac { 2 } { x ^ { 3 } } - \frac { 3 } { x ^ { 2 } } )$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-\frac{Ux^{2}}{e\left(3x-2\right)}\text{, }&x\neq \frac{2}{3}\text{ and }x\neq 0\\p\in \mathrm{C}\text{, }&x=\frac{2}{3}\text{ and }U=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{3}, the least common multiple of x^{3},x^{2}.

$$Ux^{3}=exp\left(\frac{2}{x^{3}}-\frac{3}{x^{2}}\right)x^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$Ux^{3}=ex^{4}p\left(\frac{2}{x^{3}}-\frac{3}{x^{2}}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{3} and x^{2} is x^{3}. Multiply \frac{3}{x^{2}} times \frac{x}{x}.

$$Ux^{3}=ex^{4}p\left(\frac{2}{x^{3}}-\frac{3x}{x^{3}}\right)$$

Since \frac{2}{x^{3}} and \frac{3x}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$Ux^{3}=ex^{4}p\times \frac{2-3x}{x^{3}}$$

Express e\times \frac{2-3x}{x^{3}} as a single fraction.

$$Ux^{3}=\frac{e\left(2-3x\right)}{x^{3}}x^{4}p$$

Use the distributive property to multiply e by 2-3x.

$$Ux^{3}=\frac{2e-3ex}{x^{3}}x^{4}p$$

Express \frac{2e-3ex}{x^{3}}x^{4} as a single fraction.

$$Ux^{3}=\frac{\left(2e-3ex\right)x^{4}}{x^{3}}p$$

Cancel out x^{3} in both numerator and denominator.

$$Ux^{3}=x\left(-3ex+2e\right)p$$

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

$$x\left(-3ex+2e\right)p=Ux^{3}$$

Use the distributive property to multiply x by -3ex+2e.

$$\left(-3ex^{2}+2xe\right)p=Ux^{3}$$

The equation is in standard form.

$$\left(2ex-3ex^{2}\right)p=Ux^{3}$$

Divide both sides by -3ex^{2}+2xe.

$$\frac{\left(2ex-3ex^{2}\right)p}{2ex-3ex^{2}}=\frac{Ux^{3}}{2ex-3ex^{2}}$$

Dividing by -3ex^{2}+2xe undoes the multiplication by -3ex^{2}+2xe.

$$p=\frac{Ux^{3}}{2ex-3ex^{2}}$$

Divide Ux^{3} by -3ex^{2}+2xe.

$$p=\frac{Ux^{2}}{e\left(2-3x\right)}$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{Ux^{2}}{e\left(3x-2\right)}\text{, }&x\neq \frac{2}{3}\text{ and }x\neq 0\\p\in \mathrm{R}\text{, }&x=\frac{2}{3}\text{ and }U=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{3}, the least common multiple of x^{3},x^{2}.

$$Ux^{3}=exp\left(\frac{2}{x^{3}}-\frac{3}{x^{2}}\right)x^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$Ux^{3}=ex^{4}p\left(\frac{2}{x^{3}}-\frac{3}{x^{2}}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{3} and x^{2} is x^{3}. Multiply \frac{3}{x^{2}} times \frac{x}{x}.

$$Ux^{3}=ex^{4}p\left(\frac{2}{x^{3}}-\frac{3x}{x^{3}}\right)$$

Since \frac{2}{x^{3}} and \frac{3x}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$Ux^{3}=ex^{4}p\times \frac{2-3x}{x^{3}}$$

Express e\times \frac{2-3x}{x^{3}} as a single fraction.

$$Ux^{3}=\frac{e\left(2-3x\right)}{x^{3}}x^{4}p$$

Use the distributive property to multiply e by 2-3x.

$$Ux^{3}=\frac{2e-3ex}{x^{3}}x^{4}p$$

Express \frac{2e-3ex}{x^{3}}x^{4} as a single fraction.

$$Ux^{3}=\frac{\left(2e-3ex\right)x^{4}}{x^{3}}p$$

Cancel out x^{3} in both numerator and denominator.

$$Ux^{3}=x\left(-3ex+2e\right)p$$

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

$$x\left(-3ex+2e\right)p=Ux^{3}$$

Use the distributive property to multiply x by -3ex+2e.

$$\left(-3ex^{2}+2xe\right)p=Ux^{3}$$

The equation is in standard form.

$$\left(2ex-3ex^{2}\right)p=Ux^{3}$$

Divide both sides by -3ex^{2}+2xe.

$$\frac{\left(2ex-3ex^{2}\right)p}{2ex-3ex^{2}}=\frac{Ux^{3}}{2ex-3ex^{2}}$$

Dividing by -3ex^{2}+2xe undoes the multiplication by -3ex^{2}+2xe.

$$p=\frac{Ux^{3}}{2ex-3ex^{2}}$$

Divide Ux^{3} by -3ex^{2}+2xe.

$$p=\frac{Ux^{2}}{e\left(2-3x\right)}$$

Solve for U

$$U=-\frac{ep\left(3x-2\right)}{x^{2}}$$

$$x\neq 0$$