Solve 2y+y/3-2y+y+y/20-9=

$$\frac { 2 y + y } { 3 - 2 y } + \frac { y + y } { 20 - 9 } =$$

Evaluate

$$\frac{y\left(39-4y\right)}{11\left(3-2y\right)}$$

Short Solution Steps

Combine 2y and y to get 3y.

$$\frac{3y}{3-2y}+\frac{y+y}{20-9}$$

Combine y and y to get 2y.

$$\frac{3y}{3-2y}+\frac{2y}{20-9}$$

Subtract 9 from 20 to get 11.

$$\frac{3y}{3-2y}+\frac{2y}{11}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3-2y and 11 is 11\left(-2y+3\right). Multiply \frac{3y}{3-2y} times \frac{11}{11}. Multiply \frac{2y}{11} times \frac{-2y+3}{-2y+3}.

$$\frac{11\times 3y}{11\left(-2y+3\right)}+\frac{2y\left(-2y+3\right)}{11\left(-2y+3\right)}$$

Since \frac{11\times 3y}{11\left(-2y+3\right)} and \frac{2y\left(-2y+3\right)}{11\left(-2y+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{11\times 3y+2y\left(-2y+3\right)}{11\left(-2y+3\right)}$$

Do the multiplications in 11\times 3y+2y\left(-2y+3\right).

$$\frac{33y-4y^{2}+6y}{11\left(-2y+3\right)}$$

Combine like terms in 33y-4y^{2}+6y.

$$\frac{39y-4y^{2}}{11\left(-2y+3\right)}$$

Expand 11\left(-2y+3\right).

$$\frac{39y-4y^{2}}{-22y+33}$$

Expand

$$-\frac{4y^{2}-39y}{11\left(3-2y\right)}$$

Short Solution Steps

Combine 2y and y to get 3y.

$$\frac{3y}{3-2y}+\frac{y+y}{20-9}$$

Combine y and y to get 2y.

$$\frac{3y}{3-2y}+\frac{2y}{20-9}$$

Subtract 9 from 20 to get 11.

$$\frac{3y}{3-2y}+\frac{2y}{11}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3-2y and 11 is 11\left(-2y+3\right). Multiply \frac{3y}{3-2y} times \frac{11}{11}. Multiply \frac{2y}{11} times \frac{-2y+3}{-2y+3}.

$$\frac{11\times 3y}{11\left(-2y+3\right)}+\frac{2y\left(-2y+3\right)}{11\left(-2y+3\right)}$$

Since \frac{11\times 3y}{11\left(-2y+3\right)} and \frac{2y\left(-2y+3\right)}{11\left(-2y+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{11\times 3y+2y\left(-2y+3\right)}{11\left(-2y+3\right)}$$

Do the multiplications in 11\times 3y+2y\left(-2y+3\right).

$$\frac{33y-4y^{2}+6y}{11\left(-2y+3\right)}$$

Combine like terms in 33y-4y^{2}+6y.

$$\frac{39y-4y^{2}}{11\left(-2y+3\right)}$$

Expand 11\left(-2y+3\right).

$$\frac{39y-4y^{2}}{-22y+33}$$