Solve 84:y=x+4/x^2-x-20

$$84 : y = \frac { x + 4 } { x ^ { 2 } - x - 20 }$$

Solve for y (complex solution)

$$y=84\left(x-5\right)$$

$$x\neq -4\text{ and }x\neq 5$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y\left(x-5\right)\left(x+4\right), the least common multiple of y,x^{2}-x-20.

$$\left(x-5\right)\left(x+4\right)\times 84=y\left(x+4\right)$$

Use the distributive property to multiply x-5 by x+4 and combine like terms.

$$\left(x^{2}-x-20\right)\times 84=y\left(x+4\right)$$

Use the distributive property to multiply x^{2}-x-20 by 84.

$$84x^{2}-84x-1680=y\left(x+4\right)$$

Use the distributive property to multiply y by x+4.

$$84x^{2}-84x-1680=yx+4y$$

Swap sides so that all variable terms are on the left hand side.

$$yx+4y=84x^{2}-84x-1680$$

Combine all terms containing y.

$$\left(x+4\right)y=84x^{2}-84x-1680$$

Divide both sides by 4+x.

$$\frac{\left(x+4\right)y}{x+4}=\frac{84\left(x-5\right)\left(x+4\right)}{x+4}$$

Dividing by 4+x undoes the multiplication by 4+x.

$$y=\frac{84\left(x-5\right)\left(x+4\right)}{x+4}$$

Divide 84\left(-5+x\right)\left(4+x\right) by 4+x.

$$y=84x-420$$

Variable y cannot be equal to 0.

$$y=84x-420\text{, }y\neq 0$$

Solve for y

$$y=84\left(x-5\right)$$

$$x\neq 5\text{ and }x\neq -4$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y\left(x-5\right)\left(x+4\right), the least common multiple of y,x^{2}-x-20.

$$\left(x-5\right)\left(x+4\right)\times 84=y\left(x+4\right)$$

Use the distributive property to multiply x-5 by x+4 and combine like terms.

$$\left(x^{2}-x-20\right)\times 84=y\left(x+4\right)$$

Use the distributive property to multiply x^{2}-x-20 by 84.

$$84x^{2}-84x-1680=y\left(x+4\right)$$

Use the distributive property to multiply y by x+4.

$$84x^{2}-84x-1680=yx+4y$$

Swap sides so that all variable terms are on the left hand side.

$$yx+4y=84x^{2}-84x-1680$$

Combine all terms containing y.

$$\left(x+4\right)y=84x^{2}-84x-1680$$

Divide both sides by x+4.

$$\frac{\left(x+4\right)y}{x+4}=\frac{84\left(x-5\right)\left(x+4\right)}{x+4}$$

Dividing by x+4 undoes the multiplication by x+4.

$$y=\frac{84\left(x-5\right)\left(x+4\right)}{x+4}$$

Divide 84\left(-5+x\right)\left(4+x\right) by x+4.

$$y=84x-420$$

Variable y cannot be equal to 0.

$$y=84x-420\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=\frac{y+420}{84}$$

$$y\neq -756\text{ and }y\neq 0$$

Solve for x

$$x=\frac{y+420}{84}$$

$$y\neq 0\text{ and }y\neq -756$$