Solve 3/a+a+5a/a+b=

$$\frac { 3 } { a + a } + \frac { 5 a } { a + b } =$$

Evaluate

$$\frac{10a^{2}+3a+3b}{2a\left(a+b\right)}$$

Short Solution Steps

Combine a and a to get 2a.

$$\frac{3}{2a}+\frac{5a}{a+b}$$

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

$$\frac{3\left(a+b\right)}{2a\left(a+b\right)}+\frac{5a\times 2a}{2a\left(a+b\right)}$$

Since \frac{3\left(a+b\right)}{2a\left(a+b\right)} and \frac{5a\times 2a}{2a\left(a+b\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\left(a+b\right)+5a\times 2a}{2a\left(a+b\right)}$$

Do the multiplications in 3\left(a+b\right)+5a\times 2a.

$$\frac{3a+3b+10a^{2}}{2a\left(a+b\right)}$$

Expand 2a\left(a+b\right).

$$\frac{3a+3b+10a^{2}}{2a^{2}+2ab}$$

Differentiate w.r.t. a

$$\frac{10ba^{2}-3b^{2}-6ab-3a^{2}}{2\left(a\left(a+b\right)\right)^{2}}$$