Solve x^2+4x+3edivhx=x+1

$${ x }^{ 2 } +4x+3e \div hx = x+1$$

Solve for h

$$h=-\frac{3ex}{x^{2}+3x-1}$$

$$x\neq 0\text{ and }x\neq \frac{\sqrt{13}-3}{2}\text{ and }x\neq \frac{-\sqrt{13}-3}{2}$$

Steps for Solving Linear Equation

Variable h cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by h.

$$hx^{2}+4xh+3ex=hx+h$$

Subtract hx from both sides.

$$hx^{2}+4xh+3ex-hx=h$$

Combine 4xh and -hx to get 3xh.

$$hx^{2}+3xh+3ex=h$$

Subtract h from both sides.

$$hx^{2}+3xh+3ex-h=0$$

Subtract 3ex from both sides. Anything subtracted from zero gives its negation.

$$hx^{2}+3xh-h=-3ex$$

Combine all terms containing h.

$$\left(x^{2}+3x-1\right)h=-3ex$$

Divide both sides by x^{2}+3x-1.

$$\frac{\left(x^{2}+3x-1\right)h}{x^{2}+3x-1}=-\frac{3ex}{x^{2}+3x-1}$$

Dividing by x^{2}+3x-1 undoes the multiplication by x^{2}+3x-1.

$$h=-\frac{3ex}{x^{2}+3x-1}$$

Variable h cannot be equal to 0.

$$h=-\frac{3ex}{x^{2}+3x-1}\text{, }h\neq 0$$

Solve for x

$$x=\frac{\sqrt{13h^{2}+18eh+9e^{2}}-3h-3e}{2h}$$

$$x=-\frac{\sqrt{13h^{2}+18eh+9e^{2}}+3h+3e}{2h}\text{, }h\neq 0$$