Solve x+2/x+x=74/y

$$\frac { x + 2 } { x } + x = \frac { 74 } { y }$$

Solve for y (complex solution)

$$y=\frac{74x}{x^{2}+x+2}$$

$$x\neq 0\text{ and }x\neq \frac{-1+\sqrt{7}i}{2}\text{ and }x\neq \frac{-\sqrt{7}i-1}{2}$$

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 xy, the least common multiple of x,y.

$$y\left(x+2\right)+xyx=x\times 74$$

Use the distributive property to multiply y by x+2.

$$yx+2y+xyx=x\times 74$$

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

$$yx+2y+x^{2}y=x\times 74$$

Combine all terms containing y.

$$\left(x+2+x^{2}\right)y=x\times 74$$

The equation is in standard form.

$$\left(x^{2}+x+2\right)y=74x$$

Divide both sides by x^{2}+x+2.

$$\frac{\left(x^{2}+x+2\right)y}{x^{2}+x+2}=\frac{74x}{x^{2}+x+2}$$

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

$$y=\frac{74x}{x^{2}+x+2}$$

Variable y cannot be equal to 0.

$$y=\frac{74x}{x^{2}+x+2}\text{, }y\neq 0$$

Solve for y

$$y=\frac{74x}{x^{2}+x+2}$$

$$x\neq 0$$

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 xy, the least common multiple of x,y.

$$y\left(x+2\right)+xyx=x\times 74$$

Use the distributive property to multiply y by x+2.

$$yx+2y+xyx=x\times 74$$

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

$$yx+2y+x^{2}y=x\times 74$$

Combine all terms containing y.

$$\left(x+2+x^{2}\right)y=x\times 74$$

The equation is in standard form.

$$\left(x^{2}+x+2\right)y=74x$$

Divide both sides by x^{2}+x+2.

$$\frac{\left(x^{2}+x+2\right)y}{x^{2}+x+2}=\frac{74x}{x^{2}+x+2}$$

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

$$y=\frac{74x}{x^{2}+x+2}$$

Variable y cannot be equal to 0.

$$y=\frac{74x}{x^{2}+x+2}\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{5476-148y-7y^{2}}-y+74}{2y}$$

$$x=\frac{-\sqrt{5476-148y-7y^{2}}-y+74}{2y}\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{5476-148y-7y^{2}}-y+74}{2y}$$

$$x=\frac{-\sqrt{5476-148y-7y^{2}}-y+74}{2y}\text{, }y\neq 0\text{ and }y\geq \frac{-148\sqrt{2}-74}{7}\text{ and }y\leq \frac{148\sqrt{2}-74}{7}$$