Solve ax^a-2+x^a+bx+3=0

$$a x ^ { a - 2 } + x ^ { a } + b x + 3 = 0$$

Solve for b (complex solution)

$$b=-\frac{ax^{a-2}+x^{a}+3}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract ax^{a-2} from both sides. Anything subtracted from zero gives its negation.

$$x^{a}+bx+3=-ax^{a-2}$$

Subtract x^{a} from both sides.

$$bx+3=-ax^{a-2}-x^{a}$$

Subtract 3 from both sides.

$$bx=-ax^{a-2}-x^{a}-3$$

The equation is in standard form.

$$xb=-ax^{a-2}-x^{a}-3$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{-ax^{a-2}-x^{a}-3}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{-ax^{a-2}-x^{a}-3}{x}$$

Divide -ax^{a-2}-x^{a}-3 by x.

$$b=-\frac{ax^{a-2}+x^{a}+3}{x}$$

Solve for b

$$b=-\frac{ax^{a-2}+x^{a}+3}{x}$$

$$x>0\text{ or }\left(x<0\text{ and }Denominator(a)\text{bmod}2=1\right)$$

Steps for Solving Linear Equation

Subtract ax^{a-2} from both sides. Anything subtracted from zero gives its negation.

$$x^{a}+bx+3=-ax^{a-2}$$

Subtract x^{a} from both sides.

$$bx+3=-ax^{a-2}-x^{a}$$

Subtract 3 from both sides.

$$bx=-ax^{a-2}-x^{a}-3$$

The equation is in standard form.

$$xb=-ax^{a-2}-x^{a}-3$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{-ax^{a-2}-x^{a}-3}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{-ax^{a-2}-x^{a}-3}{x}$$

Divide -ax^{a-2}-x^{a}-3 by x.

$$b=-\frac{ax^{a-2}+x^{a}+3}{x}$$