Solve xy/x^3-3x^2div4x/x^2

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

Evaluate

$$\frac{y}{4\left(x-3\right)}$$

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

$$\frac{yx^{2}}{4\left(x^{3}-3x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{yx^{2}}{4\left(x-3\right)x^{2}}$$

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

$$\frac{y}{4\left(x-3\right)}$$

Expand the expression.

$$\frac{y}{4x-12}$$

Differentiate w.r.t. x

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