Solve 2x/y+2y/x

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

Evaluate

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

Short Solution Steps

Express 2\times \frac{x}{y} as a single fraction.

$$\frac{2x}{y}+2\times \frac{y}{x}$$

Express 2\times \frac{y}{x} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{2x}{y} times \frac{x}{x}. Multiply \frac{2y}{x} times \frac{y}{y}.

$$\frac{2xx}{xy}+\frac{2yy}{xy}$$

Since \frac{2xx}{xy} and \frac{2yy}{xy} have the same denominator, add them by adding their numerators.

$$\frac{2xx+2yy}{xy}$$

Do the multiplications in 2xx+2yy.

$$\frac{2x^{2}+2y^{2}}{xy}$$

Factor

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