Solve a^2+2ab/a+b+b+4ab/a+b

$$\frac { a ^ { 2 } + 2 a b } { a + b } + \frac { b + 4 a b } { a + b }$$

Evaluate

$$\frac{a^{2}+6ab+b}{a+b}$$

Short Solution Steps

Since \frac{a^{2}+2ab}{a+b} and \frac{b+4ab}{a+b} have the same denominator, add them by adding their numerators.

$$\frac{a^{2}+2ab+b+4ab}{a+b}$$

Combine like terms in a^{2}+2ab+b+4ab.

$$\frac{a^{2}+6ab+b}{a+b}$$

Expand

$$\frac{a^{2}+6ab+b}{a+b}$$

Short Solution Steps

Since \frac{a^{2}+2ab}{a+b} and \frac{b+4ab}{a+b} have the same denominator, add them by adding their numerators.

$$\frac{a^{2}+2ab+b+4ab}{a+b}$$

Combine like terms in a^{2}+2ab+b+4ab.

$$\frac{a^{2}+6ab+b}{a+b}$$