Solve 8y^2*(3x/-4y^3)div(-x^2y/6)

$$8 y ^ { 2 } \cdot ( \frac { 3 x } { - 4 y ^ { 3 } } ) \div ( - \frac { x ^ { 2 } y } { 6 } )$$

Evaluate

$$\frac{36}{xy^{2}}$$

Short Solution Steps

Express 8\times \frac{3x}{-4y^{3}} as a single fraction.

$$\frac{\frac{8\times 3x}{-4y^{3}}y^{2}}{-\frac{x^{2}y}{6}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{2\times 3x}{-y^{3}}y^{2}}{-\frac{x^{2}y}{6}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{6x}{-y^{3}}y^{2}}{-\frac{x^{2}y}{6}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{\frac{-6x}{y^{3}}y^{2}}{-\frac{x^{2}y}{6}}$$

Express \frac{-6x}{y^{3}}y^{2} as a single fraction.

$$\frac{\frac{-6xy^{2}}{y^{3}}}{-\frac{x^{2}y}{6}}$$

Cancel out y^{2} in both numerator and denominator.

$$\frac{\frac{-6x}{y}}{-\frac{x^{2}y}{6}}$$

Express \frac{\frac{-6x}{y}}{-\frac{x^{2}y}{6}} as a single fraction.

$$\frac{-6x}{y\left(-\frac{x^{2}y}{6}\right)}$$

Express y\left(-\frac{x^{2}y}{6}\right) as a single fraction.

$$\frac{-6x}{\frac{-yx^{2}y}{6}}$$

Divide -6x by \frac{-yx^{2}y}{6} by multiplying -6x by the reciprocal of \frac{-yx^{2}y}{6}.

$$\frac{-6x\times 6}{-yx^{2}y}$$

Cancel out x in both numerator and denominator.

$$\frac{-6\times 6}{-xyy}$$

Cancel out -1 in both numerator and denominator.

$$\frac{6\times 6}{xyy}$$

Multiply 6 and 6 to get 36.

$$\frac{36}{xyy}$$

Multiply y and y to get y^{2}.

$$\frac{36}{xy^{2}}$$

Differentiate w.r.t. x

$$-\frac{36}{\left(xy\right)^{2}}$$