Solve x/y+x+x*y=21/8

$$\frac{ x }{ y } +x+x \times y= \frac{ 21 }{ 8 }$$

Solve for x (complex solution)

$$x=\frac{21y}{8\left(y^{2}+y+1\right)}$$

$$y\neq \frac{-1+\sqrt{3}i}{2}\text{ and }y\neq \frac{-\sqrt{3}i-1}{2}\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8y, the least common multiple of y,8.

$$8x+8yx+xy\times 8y=21y$$

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

$$8x+8yx+xy^{2}\times 8=21y$$

Combine all terms containing x.

$$\left(8+8y+y^{2}\times 8\right)x=21y$$

The equation is in standard form.

$$\left(8y^{2}+8y+8\right)x=21y$$

Divide both sides by 8y^{2}+8y+8.

$$\frac{\left(8y^{2}+8y+8\right)x}{8y^{2}+8y+8}=\frac{21y}{8y^{2}+8y+8}$$

Dividing by 8y^{2}+8y+8 undoes the multiplication by 8y^{2}+8y+8.

$$x=\frac{21y}{8y^{2}+8y+8}$$

Divide 21y by 8y^{2}+8y+8.

$$x=\frac{21y}{8\left(y^{2}+y+1\right)}$$

Solve for x

$$x=\frac{21y}{8\left(y^{2}+y+1\right)}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8y, the least common multiple of y,8.

$$8x+8yx+xy\times 8y=21y$$

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

$$8x+8yx+xy^{2}\times 8=21y$$

Combine all terms containing x.

$$\left(8+8y+y^{2}\times 8\right)x=21y$$

The equation is in standard form.

$$\left(8y^{2}+8y+8\right)x=21y$$

Divide both sides by 8y^{2}+8y+8.

$$\frac{\left(8y^{2}+8y+8\right)x}{8y^{2}+8y+8}=\frac{21y}{8y^{2}+8y+8}$$

Dividing by 8y^{2}+8y+8 undoes the multiplication by 8y^{2}+8y+8.

$$x=\frac{21y}{8y^{2}+8y+8}$$

Divide 21y by 8y^{2}+8y+8.

$$x=\frac{21y}{8\left(y^{2}+y+1\right)}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{441-336x-192x^{2}}}{16x}-\frac{1}{2}+\frac{21}{16x}$$

$$y=-\frac{\sqrt{441-336x-192x^{2}}}{16x}-\frac{1}{2}+\frac{21}{16x}\text{, }x\neq 0$$

Solve for y

$$y=\frac{\sqrt{441-336x-192x^{2}}}{16x}-\frac{1}{2}+\frac{21}{16x}$$

$$y=-\frac{\sqrt{441-336x-192x^{2}}}{16x}-\frac{1}{2}+\frac{21}{16x}\text{, }x\neq 0\text{ and }x\geq -\frac{21}{8}\text{ and }x\leq \frac{7}{8}$$