Solve x^-1/y+y^-1/x

$$\frac { x ^ { - 1 } } { y } + \frac { y ^ { - 1 } } { x }$$

Evaluate

$$\frac{2}{xy}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{x^{-1}}{y} times \frac{x}{x}. Multiply \frac{y^{-1}}{x} times \frac{y}{y}.

$$\frac{x^{-1}x}{xy}+\frac{y^{-1}y}{xy}$$

Since \frac{x^{-1}x}{xy} and \frac{y^{-1}y}{xy} have the same denominator, add them by adding their numerators.

$$\frac{x^{-1}x+y^{-1}y}{xy}$$

Do the multiplications in x^{-1}x+y^{-1}y.

$$\frac{1+1}{xy}$$

Do the calculations in 1+1.

$$\frac{2}{xy}$$

Differentiate w.r.t. x

$$-\frac{2}{yx^{2}}$$