Solve frac{sqrt[3]{5x^2+66}-sqrt{x-11}}{sqrt[3]{5x^2/7+6}}=xy

$$\frac{ \sqrt[ 3 ]{ 5 { x }^{ 2 } +66 } - \sqrt{ x-11 } }{ \sqrt[ 3 ]{ \frac{ 5 { x }^{ 2 } }{ 7 } +6 } } = xy$$

Solve for y (complex solution)

$$y=\frac{\sqrt[3]{7}\left(5x^{2}+42\right)^{-\frac{1}{3}}\left(\sqrt[3]{5x^{2}+66}-\sqrt{x-11}\right)}{x}$$

$$x\neq 0\text{ and }x\neq -\frac{\sqrt{210}i}{5}\text{ and }x\neq \frac{\sqrt{210}i}{5}$$

Steps for Solving Linear Equation

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

$$xy=\frac{\sqrt[3]{5x^{2}+66}-\sqrt{x-11}}{\sqrt[3]{\frac{5x^{2}}{7}+6}}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{\sqrt[3]{7}\left(5x^{2}+42\right)^{-\frac{1}{3}}\left(\sqrt[3]{5x^{2}+66}-\sqrt{x-11}\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{\sqrt[3]{7}\left(5x^{2}+42\right)^{-\frac{1}{3}}\left(\sqrt[3]{5x^{2}+66}-\sqrt{x-11}\right)}{x}$$

Solve for y

$$y=\frac{\sqrt[3]{\frac{7}{5x^{2}+42}}\left(\sqrt[3]{5x^{2}+66}-\sqrt{x-11}\right)}{x}$$

$$x\geq 11$$

Steps for Solving Linear Equation

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

$$xy=\frac{\sqrt[3]{5x^{2}+66}-\sqrt{x-11}}{\sqrt[3]{\frac{5x^{2}}{7}+6}}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{\sqrt[3]{7}\left(\sqrt[3]{5x^{2}+66}-\sqrt{x-11}\right)}{\sqrt[3]{5x^{2}+42}x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{\sqrt[3]{7}\left(\sqrt[3]{5x^{2}+66}-\sqrt{x-11}\right)}{\sqrt[3]{5x^{2}+42}x}$$