Solve 4p/p+1+2/p+2

$$\frac { 4 p } { p + 1 } + \frac { 2 } { p + 2 }$$

Evaluate

$$\frac{2\left(2p^{2}+5p+1\right)}{\left(p+1\right)\left(p+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p+1 and p+2 is \left(p+1\right)\left(p+2\right). Multiply \frac{4p}{p+1} times \frac{p+2}{p+2}. Multiply \frac{2}{p+2} times \frac{p+1}{p+1}.

$$\frac{4p\left(p+2\right)}{\left(p+1\right)\left(p+2\right)}+\frac{2\left(p+1\right)}{\left(p+1\right)\left(p+2\right)}$$

Since \frac{4p\left(p+2\right)}{\left(p+1\right)\left(p+2\right)} and \frac{2\left(p+1\right)}{\left(p+1\right)\left(p+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{4p\left(p+2\right)+2\left(p+1\right)}{\left(p+1\right)\left(p+2\right)}$$

Do the multiplications in 4p\left(p+2\right)+2\left(p+1\right).

$$\frac{4p^{2}+8p+2p+2}{\left(p+1\right)\left(p+2\right)}$$

Combine like terms in 4p^{2}+8p+2p+2.

$$\frac{4p^{2}+10p+2}{\left(p+1\right)\left(p+2\right)}$$

Expand \left(p+1\right)\left(p+2\right).

$$\frac{4p^{2}+10p+2}{p^{2}+3p+2}$$

Factor

$$\frac{4\left(p-\frac{-\sqrt{17}-5}{4}\right)\left(p-\frac{\sqrt{17}-5}{4}\right)}{\left(p+1\right)\left(p+2\right)}$$