Solve pcx1=x^-1-5x^2+4

$$p c x 1 = x ^ { - 1 } - 5 x ^ { 2 } + 4$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=-\frac{5x^{3}-4x-1}{pxx_{1}}\text{, }&x\neq 0\text{ and }x_{1}\neq 0\text{ and }p\neq 0\\c\in \mathrm{C}\text{, }&\left(x=1\text{ and }x_{1}=0\right)\text{ or }\left(x=-\frac{\sqrt{5}}{10}-\frac{1}{2}\text{ and }x_{1}=0\right)\text{ or }\left(x=\frac{\sqrt{5}}{10}-\frac{1}{2}\text{ and }x_{1}=0\right)\text{ or }\left(p=0\text{ and }x_{1}\neq 0\text{ and }x=\frac{\sqrt{5}}{10}-\frac{1}{2}\right)\text{ or }\left(p=0\text{ and }x_{1}\neq 0\text{ and }x=-\frac{\sqrt{5}}{10}-\frac{1}{2}\right)\text{ or }\left(p=0\text{ and }x_{1}\neq 0\text{ and }x=1\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$cpx_{1}=-5x^{2}+4+\frac{1}{x}$$

Multiply both sides of the equation by x.

$$cpx_{1}x=-5x^{2}x+x\times 4+1$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$cpx_{1}x=-5x^{3}+x\times 4+1$$

The equation is in standard form.

$$pxx_{1}c=1+4x-5x^{3}$$

Divide both sides by px_{1}x.

$$\frac{pxx_{1}c}{pxx_{1}}=\frac{1+4x-5x^{3}}{pxx_{1}}$$

Dividing by px_{1}x undoes the multiplication by px_{1}x.

$$c=\frac{1+4x-5x^{3}}{pxx_{1}}$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-\frac{5x^{3}-4x-1}{cxx_{1}}\text{, }&x\neq 0\text{ and }x_{1}\neq 0\text{ and }c\neq 0\\p\in \mathrm{C}\text{, }&\left(x=1\text{ and }x_{1}=0\right)\text{ or }\left(x=-\frac{\sqrt{5}}{10}-\frac{1}{2}\text{ and }x_{1}=0\right)\text{ or }\left(x=\frac{\sqrt{5}}{10}-\frac{1}{2}\text{ and }x_{1}=0\right)\text{ or }\left(c=0\text{ and }x_{1}\neq 0\text{ and }x=\frac{\sqrt{5}}{10}-\frac{1}{2}\right)\text{ or }\left(c=0\text{ and }x_{1}\neq 0\text{ and }x=-\frac{\sqrt{5}}{10}-\frac{1}{2}\right)\text{ or }\left(c=0\text{ and }x_{1}\neq 0\text{ and }x=1\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$cpx_{1}=-5x^{2}+4+\frac{1}{x}$$

Multiply both sides of the equation by x.

$$cpx_{1}x=-5x^{2}x+x\times 4+1$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$cpx_{1}x=-5x^{3}+x\times 4+1$$

The equation is in standard form.

$$cxx_{1}p=1+4x-5x^{3}$$

Divide both sides by cx_{1}x.

$$\frac{cxx_{1}p}{cxx_{1}}=\frac{1+4x-5x^{3}}{cxx_{1}}$$

Dividing by cx_{1}x undoes the multiplication by cx_{1}x.

$$p=\frac{1+4x-5x^{3}}{cxx_{1}}$$

Solve for c

$$\left\{\begin{matrix}c=-\frac{5x^{3}-4x-1}{pxx_{1}}\text{, }&x\neq 0\text{ and }x_{1}\neq 0\text{ and }p\neq 0\\c\in \mathrm{R}\text{, }&\left(x=-\frac{\sqrt{5}}{10}-\frac{1}{2}\text{ and }x_{1}=0\right)\text{ or }\left(x=\frac{\sqrt{5}}{10}-\frac{1}{2}\text{ and }x_{1}=0\right)\text{ or }\left(x=1\text{ and }x_{1}=0\right)\text{ or }\left(p=0\text{ and }x_{1}\neq 0\text{ and }x=1\right)\text{ or }\left(p=0\text{ and }x_{1}\neq 0\text{ and }x=\frac{\sqrt{5}}{10}-\frac{1}{2}\right)\text{ or }\left(p=0\text{ and }x_{1}\neq 0\text{ and }x=-\frac{\sqrt{5}}{10}-\frac{1}{2}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$cpx_{1}=-5x^{2}+4+\frac{1}{x}$$

Multiply both sides of the equation by x.

$$cpx_{1}x=-5x^{2}x+x\times 4+1$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$cpx_{1}x=-5x^{3}+x\times 4+1$$

The equation is in standard form.

$$pxx_{1}c=1+4x-5x^{3}$$

Divide both sides by px_{1}x.

$$\frac{pxx_{1}c}{pxx_{1}}=\frac{1+4x-5x^{3}}{pxx_{1}}$$

Dividing by px_{1}x undoes the multiplication by px_{1}x.

$$c=\frac{1+4x-5x^{3}}{pxx_{1}}$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{5x^{3}-4x-1}{cxx_{1}}\text{, }&x\neq 0\text{ and }x_{1}\neq 0\text{ and }c\neq 0\\p\in \mathrm{R}\text{, }&\left(x=-\frac{\sqrt{5}}{10}-\frac{1}{2}\text{ and }x_{1}=0\right)\text{ or }\left(x=\frac{\sqrt{5}}{10}-\frac{1}{2}\text{ and }x_{1}=0\right)\text{ or }\left(x=1\text{ and }x_{1}=0\right)\text{ or }\left(c=0\text{ and }x_{1}\neq 0\text{ and }x=1\right)\text{ or }\left(c=0\text{ and }x_{1}\neq 0\text{ and }x=\frac{\sqrt{5}}{10}-\frac{1}{2}\right)\text{ or }\left(c=0\text{ and }x_{1}\neq 0\text{ and }x=-\frac{\sqrt{5}}{10}-\frac{1}{2}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$cpx_{1}=-5x^{2}+4+\frac{1}{x}$$

Multiply both sides of the equation by x.

$$cpx_{1}x=-5x^{2}x+x\times 4+1$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$cpx_{1}x=-5x^{3}+x\times 4+1$$

The equation is in standard form.

$$cxx_{1}p=1+4x-5x^{3}$$

Divide both sides by cx_{1}x.

$$\frac{cxx_{1}p}{cxx_{1}}=\frac{1+4x-5x^{3}}{cxx_{1}}$$

Dividing by cx_{1}x undoes the multiplication by cx_{1}x.

$$p=\frac{1+4x-5x^{3}}{cxx_{1}}$$