Solve 3/-y-(4/12-9/-6)

$$\frac { 3 } { - y } - ( \frac { 4 } { 12 } - \frac { 9 } { - 6 } )$$

Evaluate

$$-\frac{11}{6}-\frac{3}{y}$$

Short Solution Steps

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{3}{-y}-\left(\frac{1}{3}-\frac{9}{-6}\right)$$

Reduce the fraction \frac{9}{-6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{-y}-\left(\frac{1}{3}-\left(-\frac{3}{2}\right)\right)$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$\frac{3}{-y}-\left(\frac{1}{3}+\frac{3}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{3}{-y}-\left(\frac{2}{6}+\frac{9}{6}\right)$$

Since \frac{2}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{3}{-y}-\frac{2+9}{6}$$

Add 2 and 9 to get 11.

$$\frac{3}{-y}-\frac{11}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of -y and 6 is 6y. Multiply \frac{3}{-y} times \frac{-6}{-6}. Multiply \frac{11}{6} times \frac{y}{y}.

$$\frac{3\left(-6\right)}{6y}-\frac{11y}{6y}$$

Since \frac{3\left(-6\right)}{6y} and \frac{11y}{6y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-6\right)-11y}{6y}$$

Do the multiplications in 3\left(-6\right)-11y.

$$\frac{-18-11y}{6y}$$

Expand

$$-\frac{11}{6}-\frac{3}{y}$$

Short Solution Steps

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{3}{-y}-\left(\frac{1}{3}-\frac{9}{-6}\right)$$

Reduce the fraction \frac{9}{-6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{-y}-\left(\frac{1}{3}-\left(-\frac{3}{2}\right)\right)$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$\frac{3}{-y}-\left(\frac{1}{3}+\frac{3}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{3}{-y}-\left(\frac{2}{6}+\frac{9}{6}\right)$$

Since \frac{2}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{3}{-y}-\frac{2+9}{6}$$

Add 2 and 9 to get 11.

$$\frac{3}{-y}-\frac{11}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of -y and 6 is 6y. Multiply \frac{3}{-y} times \frac{-6}{-6}. Multiply \frac{11}{6} times \frac{y}{y}.

$$\frac{3\left(-6\right)}{6y}-\frac{11y}{6y}$$

Since \frac{3\left(-6\right)}{6y} and \frac{11y}{6y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-6\right)-11y}{6y}$$

Do the multiplications in 3\left(-6\right)-11y.

$$\frac{-18-11y}{6y}$$