Solve frac{2a^{2}}{x^2y^2}div-a/xy*x^2/2a^2=

$$\frac { 2 a ^ { 2 } } { x ^ { 2 } y ^ { 2 } } \div \frac { - a } { x y } \times \frac { x ^ { 2 } } { 2 a ^ { 2 } } =$$

Evaluate

$$-\frac{x}{ay}$$

Short Solution Steps

Divide \frac{2a^{2}}{x^{2}y^{2}} by \frac{-a}{xy} by multiplying \frac{2a^{2}}{x^{2}y^{2}} by the reciprocal of \frac{-a}{xy}.

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

Cancel out xy in both numerator and denominator.

$$\frac{2a^{2}}{\left(-a\right)xy}\times \frac{x^{2}}{2a^{2}}$$

Factor the expressions that are not already factored in \frac{2a^{2}}{\left(-a\right)xy}.

$$\frac{2a^{2}}{-axy}\times \frac{x^{2}}{2a^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{2a}{-xy}\times \frac{x^{2}}{2a^{2}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-2a}{xy}\times \frac{x^{2}}{2a^{2}}$$

Multiply \frac{-2a}{xy} times \frac{x^{2}}{2a^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2ax^{2}}{xy\times 2a^{2}}$$

Cancel out 2ax in both numerator and denominator.

$$\frac{-x}{ay}$$

Differentiate w.r.t. x

$$-\frac{1}{ay}$$