Solve 32y/x^2+16/x=5y

$$\frac { 32 y } { x ^ { 2 } } + \frac { 16 } { x } = 5 y$$

Solve for y (complex solution)

$$y=-\frac{16x}{32-5x^{2}}$$

$$x\neq -\frac{4\sqrt{10}}{5}\text{ and }x\neq \frac{4\sqrt{10}}{5}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}, the least common multiple of x^{2},x.

$$32y+x\times 16=5yx^{2}$$

Subtract 5yx^{2} from both sides.

$$32y+x\times 16-5yx^{2}=0$$

Subtract x\times 16 from both sides. Anything subtracted from zero gives its negation.

$$32y-5yx^{2}=-x\times 16$$

Combine all terms containing y.

$$\left(32-5x^{2}\right)y=-x\times 16$$

The equation is in standard form.

$$\left(32-5x^{2}\right)y=-16x$$

Divide both sides by -5x^{2}+32.

$$\frac{\left(32-5x^{2}\right)y}{32-5x^{2}}=-\frac{16x}{32-5x^{2}}$$

Dividing by -5x^{2}+32 undoes the multiplication by -5x^{2}+32.

$$y=-\frac{16x}{32-5x^{2}}$$

Solve for y

$$y=-\frac{16x}{32-5x^{2}}$$

$$|x|\neq \frac{4\sqrt{10}}{5}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}, the least common multiple of x^{2},x.

$$32y+x\times 16=5yx^{2}$$

Subtract 5yx^{2} from both sides.

$$32y+x\times 16-5yx^{2}=0$$

Subtract x\times 16 from both sides. Anything subtracted from zero gives its negation.

$$32y-5yx^{2}=-x\times 16$$

Combine all terms containing y.

$$\left(32-5x^{2}\right)y=-x\times 16$$

The equation is in standard form.

$$\left(32-5x^{2}\right)y=-16x$$

Divide both sides by -5x^{2}+32.

$$\frac{\left(32-5x^{2}\right)y}{32-5x^{2}}=-\frac{16x}{32-5x^{2}}$$

Dividing by -5x^{2}+32 undoes the multiplication by -5x^{2}+32.

$$y=-\frac{16x}{32-5x^{2}}$$

Solve for x

$$x=-\frac{4\left(\sqrt{2\left(5y^{2}+2\right)}-2\right)}{5y}$$

$$x=\frac{4\sqrt{2}\left(\sqrt{5y^{2}+2}+\sqrt{2}\right)}{5y}\text{, }y\neq 0$$