Solve 25/x+53=62/y^2

$$\frac { 25 } { x } + 53 = \frac { 62 } { y ^ { 2 } }$$

Solve for x (complex solution)

$$x=-\frac{25y^{2}}{53y^{2}-62}$$

$$y\neq 0\text{ and }y\neq -\frac{\sqrt{3286}}{53}\text{ and }y\neq \frac{\sqrt{3286}}{53}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy^{2}, the least common multiple of x,y^{2}.

$$y^{2}\times 25+xy^{2}\times 53=x\times 62$$

Subtract x\times 62 from both sides.

$$y^{2}\times 25+xy^{2}\times 53-x\times 62=0$$

Multiply -1 and 62 to get -62.

$$y^{2}\times 25+xy^{2}\times 53-62x=0$$

Subtract y^{2}\times 25 from both sides. Anything subtracted from zero gives its negation.

$$xy^{2}\times 53-62x=-y^{2}\times 25$$

Combine all terms containing x.

$$\left(y^{2}\times 53-62\right)x=-y^{2}\times 25$$

The equation is in standard form.

$$\left(53y^{2}-62\right)x=-25y^{2}$$

Divide both sides by 53y^{2}-62.

$$\frac{\left(53y^{2}-62\right)x}{53y^{2}-62}=-\frac{25y^{2}}{53y^{2}-62}$$

Dividing by 53y^{2}-62 undoes the multiplication by 53y^{2}-62.

$$x=-\frac{25y^{2}}{53y^{2}-62}$$

Variable x cannot be equal to 0.

$$x=-\frac{25y^{2}}{53y^{2}-62}\text{, }x\neq 0$$

Solve for x

$$x=-\frac{25y^{2}}{53y^{2}-62}$$

$$y\neq 0\text{ and }|y|\neq \frac{\sqrt{3286}}{53}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy^{2}, the least common multiple of x,y^{2}.

$$y^{2}\times 25+xy^{2}\times 53=x\times 62$$

Subtract x\times 62 from both sides.

$$y^{2}\times 25+xy^{2}\times 53-x\times 62=0$$

Multiply -1 and 62 to get -62.

$$y^{2}\times 25+xy^{2}\times 53-62x=0$$

Subtract y^{2}\times 25 from both sides. Anything subtracted from zero gives its negation.

$$xy^{2}\times 53-62x=-y^{2}\times 25$$

Combine all terms containing x.

$$\left(y^{2}\times 53-62\right)x=-y^{2}\times 25$$

The equation is in standard form.

$$\left(53y^{2}-62\right)x=-25y^{2}$$

Divide both sides by 53y^{2}-62.

$$\frac{\left(53y^{2}-62\right)x}{53y^{2}-62}=-\frac{25y^{2}}{53y^{2}-62}$$

Dividing by 53y^{2}-62 undoes the multiplication by 53y^{2}-62.

$$x=-\frac{25y^{2}}{53y^{2}-62}$$

Variable x cannot be equal to 0.

$$x=-\frac{25y^{2}}{53y^{2}-62}\text{, }x\neq 0$$

Solve for y (complex solution)

$$y=-i\left(-53x-25\right)^{-\frac{1}{2}}\sqrt{62x}$$

$$y=i\left(-53x-25\right)^{-\frac{1}{2}}\sqrt{62x}\text{, }x\neq 0\text{ and }x\neq -\frac{25}{53}$$

Solve for y

$$y=\sqrt{\frac{62x}{53x+25}}$$

$$y=-\sqrt{\frac{62x}{53x+25}}\text{, }x<-\frac{25}{53}\text{ or }x>0$$