Solve A(x)=x^4+4x+5*x*B(x)=x+2

$$A ( x ) = x ^ { 4 } + 4 x + 5 \cdot x \cdot B ( x ) = x + 2$$

Solve for B

$$B=-\frac{x^{4}+3x-2}{5x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$x^{4}+4x+5x^{2}B=x+2$$

Subtract x^{4} from both sides.

$$4x+5x^{2}B=x+2-x^{4}$$

Subtract 4x from both sides.

$$5x^{2}B=x+2-x^{4}-4x$$

Combine x and -4x to get -3x.

$$5x^{2}B=-3x+2-x^{4}$$

The equation is in standard form.

$$5x^{2}B=2-3x-x^{4}$$

Divide both sides by 5x^{2}.

$$\frac{5x^{2}B}{5x^{2}}=\frac{2-3x-x^{4}}{5x^{2}}$$

Dividing by 5x^{2} undoes the multiplication by 5x^{2}.

$$B=\frac{2-3x-x^{4}}{5x^{2}}$$