Solve 14-2y/2y-5+6y-2/2y+3

$$\frac { 14 - 2 y } { 2 y - 5 } + \frac { 6 y - 2 } { 2 y + 3 }$$

Evaluate

$$\frac{4\left(2y^{2}-3y+13\right)}{\left(2y-5\right)\left(2y+3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2y-5 and 2y+3 is \left(2y-5\right)\left(2y+3\right). Multiply \frac{14-2y}{2y-5} times \frac{2y+3}{2y+3}. Multiply \frac{6y-2}{2y+3} times \frac{2y-5}{2y-5}.

$$\frac{\left(14-2y\right)\left(2y+3\right)}{\left(2y-5\right)\left(2y+3\right)}+\frac{\left(6y-2\right)\left(2y-5\right)}{\left(2y-5\right)\left(2y+3\right)}$$

Since \frac{\left(14-2y\right)\left(2y+3\right)}{\left(2y-5\right)\left(2y+3\right)} and \frac{\left(6y-2\right)\left(2y-5\right)}{\left(2y-5\right)\left(2y+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(14-2y\right)\left(2y+3\right)+\left(6y-2\right)\left(2y-5\right)}{\left(2y-5\right)\left(2y+3\right)}$$

Do the multiplications in \left(14-2y\right)\left(2y+3\right)+\left(6y-2\right)\left(2y-5\right).

$$\frac{28y+42-4y^{2}-6y+12y^{2}-30y-4y+10}{\left(2y-5\right)\left(2y+3\right)}$$

Combine like terms in 28y+42-4y^{2}-6y+12y^{2}-30y-4y+10.

$$\frac{-12y+52+8y^{2}}{\left(2y-5\right)\left(2y+3\right)}$$

Expand \left(2y-5\right)\left(2y+3\right).

$$\frac{-12y+52+8y^{2}}{4y^{2}-4y-15}$$

Expand

$$\frac{4\left(2y^{2}-3y+13\right)}{\left(2y-5\right)\left(2y+3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2y-5 and 2y+3 is \left(2y-5\right)\left(2y+3\right). Multiply \frac{14-2y}{2y-5} times \frac{2y+3}{2y+3}. Multiply \frac{6y-2}{2y+3} times \frac{2y-5}{2y-5}.

$$\frac{\left(14-2y\right)\left(2y+3\right)}{\left(2y-5\right)\left(2y+3\right)}+\frac{\left(6y-2\right)\left(2y-5\right)}{\left(2y-5\right)\left(2y+3\right)}$$

Since \frac{\left(14-2y\right)\left(2y+3\right)}{\left(2y-5\right)\left(2y+3\right)} and \frac{\left(6y-2\right)\left(2y-5\right)}{\left(2y-5\right)\left(2y+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(14-2y\right)\left(2y+3\right)+\left(6y-2\right)\left(2y-5\right)}{\left(2y-5\right)\left(2y+3\right)}$$

Do the multiplications in \left(14-2y\right)\left(2y+3\right)+\left(6y-2\right)\left(2y-5\right).

$$\frac{28y+42-4y^{2}-6y+12y^{2}-30y-4y+10}{\left(2y-5\right)\left(2y+3\right)}$$

Combine like terms in 28y+42-4y^{2}-6y+12y^{2}-30y-4y+10.

$$\frac{-12y+52+8y^{2}}{\left(2y-5\right)\left(2y+3\right)}$$

Expand \left(2y-5\right)\left(2y+3\right).

$$\frac{-12y+52+8y^{2}}{4y^{2}-4y-15}$$