Solve y/frac{1{xy}+1}

$$\frac { y } { \frac { 1 } { x y } + 1 }$$

Evaluate

$$\frac{xy^{2}}{xy+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{xy}{xy}.

$$\frac{y}{\frac{1}{xy}+\frac{xy}{xy}}$$

Since \frac{1}{xy} and \frac{xy}{xy} have the same denominator, add them by adding their numerators.

$$\frac{y}{\frac{1+xy}{xy}}$$

Divide y by \frac{1+xy}{xy} by multiplying y by the reciprocal of \frac{1+xy}{xy}.

$$\frac{yxy}{1+xy}$$

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

$$\frac{y^{2}x}{1+xy}$$

Differentiate w.r.t. x

$$\left(\frac{y}{xy+1}\right)^{2}$$