Solve x/y^2-y/x^2-2/xy=

$$\frac { x } { y ^ { 2 } } - \frac { y } { x ^ { 2 } } - \frac { 2 } { x y } =$$

Evaluate

$$\frac{x^{3}-2xy-y^{3}}{\left(xy\right)^{2}}$$

Short Solution Steps

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

$$\frac{xx^{2}}{x^{2}y^{2}}-\frac{yy^{2}}{x^{2}y^{2}}-\frac{2}{xy}$$

Since \frac{xx^{2}}{x^{2}y^{2}} and \frac{yy^{2}}{x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx^{2}-yy^{2}}{x^{2}y^{2}}-\frac{2}{xy}$$

Do the multiplications in xx^{2}-yy^{2}.

$$\frac{x^{3}-y^{3}}{x^{2}y^{2}}-\frac{2}{xy}$$

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

$$\frac{x^{3}-y^{3}}{x^{2}y^{2}}-\frac{2xy}{x^{2}y^{2}}$$

Since \frac{x^{3}-y^{3}}{x^{2}y^{2}} and \frac{2xy}{x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{3}-y^{3}-2xy}{x^{2}y^{2}}$$

Factor

$$\frac{-\frac{y^{3}}{x^{2}}+x-\frac{2y}{x}}{y^{2}}$$