Solve x^2+2/y^-1

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

Evaluate

$$x^{2}+2y$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{y^{-1}}{y^{-1}}.

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

Since \frac{x^{2}y^{-1}}{y^{-1}} and \frac{2}{y^{-1}} have the same denominator, add them by adding their numerators.

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

Combine like terms in x^{2}y^{-1}+2.

$$\frac{x^{2}\times \frac{1}{y}+2}{y^{-1}}$$

Expand y^{-1}.

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

Divide x^{2}\times \frac{1}{y}+2 by \frac{1}{y} by multiplying x^{2}\times \frac{1}{y}+2 by the reciprocal of \frac{1}{y}.

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

Use the distributive property to multiply x^{2}\times \frac{1}{y}+2 by y.

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

Express x^{2}\times \frac{1}{y} as a single fraction.

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

Cancel out y and y.

$$x^{2}+2y$$

Differentiate w.r.t. x

$$2x$$