Solve 15x^2y/2x-ydiv3/4x^2-2xy

$$\frac { 15 x ^ { 2 } y } { 2 x - y } \div \frac { 3 } { 4 x ^ { 2 } - 2 x y }$$

Evaluate

$$10yx^{3}$$

Short Solution Steps

Divide \frac{15x^{2}y}{2x-y} by \frac{3}{4x^{2}-2xy} by multiplying \frac{15x^{2}y}{2x-y} by the reciprocal of \frac{3}{4x^{2}-2xy}.

$$\frac{15x^{2}y\left(4x^{2}-2xy\right)}{\left(2x-y\right)\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{5yx^{2}\left(4x^{2}-2xy\right)}{2x-y}$$

Factor the expressions that are not already factored.

$$\frac{2\times 5xy\left(2x-y\right)x^{2}}{2x-y}$$

Cancel out 2x-y in both numerator and denominator.

$$2\times 5xyx^{2}$$

Expand the expression.

$$10yx^{3}$$

Differentiate w.r.t. x

$$30yx^{2}$$