Solve S^primef(x)=x^2-x-3/x+1

$$S ^ { \prime } f ( x ) = \frac { x ^ { 2 } - x - 3 } { x + 1 }$$

Solve for f

$$f\in \mathrm{R}$$

$$x=\frac{\sqrt{13}+1}{2}\text{ or }x=\frac{1-\sqrt{13}}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(S)fx\left(x+1\right)=x^{2}-x-3$$

Use the distributive property to multiply \frac{\mathrm{d}}{\mathrm{d}x}(S)fx by x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(S)fx^{2}+\frac{\mathrm{d}}{\mathrm{d}x}(S)fx=x^{2}-x-3$$

Combine all terms containing f.

$$\left(\frac{\mathrm{d}}{\mathrm{d}x}(S)x^{2}+\frac{\mathrm{d}}{\mathrm{d}x}(S)x\right)f=x^{2}-x-3$$

The equation is in standard form.

$$0=x^{2}-x-3$$

This is false for any f.

$$f\in$$

Solve for S

$$S\in \mathrm{R}$$

$$x=\frac{\sqrt{13}+1}{2}\text{ or }x=\frac{1-\sqrt{13}}{2}$$