Solve 36ydiv12+18div(-27y)

$$36 y \div 12 + 18 \div ( - 27 y )$$

Evaluate

$$3y-\frac{2}{3y}$$

Short Solution Steps

Divide 36y by 12 to get 3y.

$$3y+\frac{18}{-27y}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3y times \frac{-27y}{-27y}.

$$\frac{3y\left(-27\right)y}{-27y}+\frac{18}{-27y}$$

Since \frac{3y\left(-27\right)y}{-27y} and \frac{18}{-27y} have the same denominator, add them by adding their numerators.

$$\frac{3y\left(-27\right)y+18}{-27y}$$

Do the multiplications in 3y\left(-27\right)y+18.

$$\frac{-81y^{2}+18}{-27y}$$

Factor the expressions that are not already factored in \frac{-81y^{2}+18}{-27y}.

$$\frac{9\left(-9y^{2}+2\right)}{-27y}$$

Cancel out 9 in both numerator and denominator.

$$\frac{-9y^{2}+2}{-3y}$$

Factor

$$\frac{9y^{2}-2}{3y}$$