Solve 7/2p+10+14/p+2

$$\frac { 7 } { 2 p + 10 } + \frac { 14 } { p + 2 }$$

Evaluate

$$\frac{7\left(5p+22\right)}{2\left(p+2\right)\left(p+5\right)}$$

Short Solution Steps

Factor 2p+10.

$$\frac{7}{2\left(p+5\right)}+\frac{14}{p+2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(p+5\right) and p+2 is 2\left(p+2\right)\left(p+5\right). Multiply \frac{7}{2\left(p+5\right)} times \frac{p+2}{p+2}. Multiply \frac{14}{p+2} times \frac{2\left(p+5\right)}{2\left(p+5\right)}.

$$\frac{7\left(p+2\right)}{2\left(p+2\right)\left(p+5\right)}+\frac{14\times 2\left(p+5\right)}{2\left(p+2\right)\left(p+5\right)}$$

Since \frac{7\left(p+2\right)}{2\left(p+2\right)\left(p+5\right)} and \frac{14\times 2\left(p+5\right)}{2\left(p+2\right)\left(p+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{7\left(p+2\right)+14\times 2\left(p+5\right)}{2\left(p+2\right)\left(p+5\right)}$$

Do the multiplications in 7\left(p+2\right)+14\times 2\left(p+5\right).

$$\frac{7p+14+28p+140}{2\left(p+2\right)\left(p+5\right)}$$

Combine like terms in 7p+14+28p+140.

$$\frac{35p+154}{2\left(p+2\right)\left(p+5\right)}$$

Expand 2\left(p+2\right)\left(p+5\right).

$$\frac{35p+154}{2p^{2}+14p+20}$$

Factor

$$\frac{7\left(5p+22\right)}{2\left(p+2\right)\left(p+5\right)}$$