Solve operatorname{enf}(x)=x^2-5x+7/x-2

$$\operatorname { enf } ( x ) = \frac { x ^ { 2 } - 5 x + 7 } { x - 2 }$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{-x^{2}+5x-7}{enx\left(x-2\right)}\text{, }&x\neq 2\text{ and }x\neq 0\text{ and }n\neq 0\\f\in \mathrm{C}\text{, }&\left(x=\frac{5+\sqrt{3}i}{2}\text{ or }x=\frac{-\sqrt{3}i+5}{2}\right)\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2.

$$enfx\left(x-2\right)=x^{2}-5x+7$$

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

$$enfx^{2}-2enfx=x^{2}-5x+7$$

Combine all terms containing f.

$$\left(enx^{2}-2enx\right)f=x^{2}-5x+7$$

Divide both sides by ex^{2}n-2xne.

$$\frac{\left(enx^{2}-2enx\right)f}{enx^{2}-2enx}=\frac{x^{2}-5x+7}{enx^{2}-2enx}$$

Dividing by ex^{2}n-2xne undoes the multiplication by ex^{2}n-2xne.

$$f=\frac{x^{2}-5x+7}{enx^{2}-2enx}$$

Divide x^{2}-5x+7 by ex^{2}n-2xne.

$$f=\frac{x^{2}-5x+7}{enx\left(x-2\right)}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{-x^{2}+5x-7}{efx\left(x-2\right)}\text{, }&x\neq 2\text{ and }x\neq 0\text{ and }f\neq 0\\n\in \mathrm{C}\text{, }&\left(x=\frac{5+\sqrt{3}i}{2}\text{ or }x=\frac{-\sqrt{3}i+5}{2}\right)\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2.

$$enfx\left(x-2\right)=x^{2}-5x+7$$

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

$$enfx^{2}-2enfx=x^{2}-5x+7$$

Combine all terms containing n.

$$\left(efx^{2}-2efx\right)n=x^{2}-5x+7$$

Divide both sides by ex^{2}f-2xfe.

$$\frac{\left(efx^{2}-2efx\right)n}{efx^{2}-2efx}=\frac{x^{2}-5x+7}{efx^{2}-2efx}$$

Dividing by ex^{2}f-2xfe undoes the multiplication by ex^{2}f-2xfe.

$$n=\frac{x^{2}-5x+7}{efx^{2}-2efx}$$

Divide x^{2}-5x+7 by ex^{2}f-2xfe.

$$n=\frac{x^{2}-5x+7}{efx\left(x-2\right)}$$

Solve for f

$$f=-\frac{-x^{2}+5x-7}{enx\left(x-2\right)}$$

$$x\neq 2\text{ and }x\neq 0\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2.

$$enfx\left(x-2\right)=x^{2}-5x+7$$

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

$$enfx^{2}-2enfx=x^{2}-5x+7$$

Combine all terms containing f.

$$\left(enx^{2}-2enx\right)f=x^{2}-5x+7$$

Divide both sides by ex^{2}n-2xne.

$$\frac{\left(enx^{2}-2enx\right)f}{enx^{2}-2enx}=\frac{x^{2}-5x+7}{enx^{2}-2enx}$$

Dividing by ex^{2}n-2xne undoes the multiplication by ex^{2}n-2xne.

$$f=\frac{x^{2}-5x+7}{enx^{2}-2enx}$$

Divide x^{2}-5x+7 by ex^{2}n-2xne.

$$f=\frac{x^{2}-5x+7}{enx\left(x-2\right)}$$

Solve for n

$$n=-\frac{-x^{2}+5x-7}{efx\left(x-2\right)}$$

$$x\neq 2\text{ and }x\neq 0\text{ and }f\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2.

$$enfx\left(x-2\right)=x^{2}-5x+7$$

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

$$enfx^{2}-2enfx=x^{2}-5x+7$$

Combine all terms containing n.

$$\left(efx^{2}-2efx\right)n=x^{2}-5x+7$$

Divide both sides by ex^{2}f-2xfe.

$$\frac{\left(efx^{2}-2efx\right)n}{efx^{2}-2efx}=\frac{x^{2}-5x+7}{efx^{2}-2efx}$$

Dividing by ex^{2}f-2xfe undoes the multiplication by ex^{2}f-2xfe.

$$n=\frac{x^{2}-5x+7}{efx^{2}-2efx}$$

Divide x^{2}-5x+7 by ex^{2}f-2xfe.

$$n=\frac{x^{2}-5x+7}{efx\left(x-2\right)}$$