Solve 5a/a+3+a+b/a+335/a^2+6a

$$\frac{ 5a }{ a+3 } + \frac{ a+b }{ a+3 } \frac{ 35 }{ { a }^{ 2 } +6a }$$

Evaluate

$$\frac{5\left(a^{3}+6a^{2}+7a+7b\right)}{a\left(a+3\right)\left(a+6\right)}$$

Short Solution Steps

Multiply \frac{a+b}{a+3} times \frac{35}{a^{2}+6a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5a}{a+3}+\frac{\left(a+b\right)\times 35}{\left(a+3\right)\left(a^{2}+6a\right)}$$

Factor \left(a+3\right)\left(a^{2}+6a\right).

$$\frac{5a}{a+3}+\frac{\left(a+b\right)\times 35}{a\left(a+3\right)\left(a+6\right)}$$

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

$$\frac{5aa\left(a+6\right)}{a\left(a+3\right)\left(a+6\right)}+\frac{\left(a+b\right)\times 35}{a\left(a+3\right)\left(a+6\right)}$$

Since \frac{5aa\left(a+6\right)}{a\left(a+3\right)\left(a+6\right)} and \frac{\left(a+b\right)\times 35}{a\left(a+3\right)\left(a+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{5aa\left(a+6\right)+\left(a+b\right)\times 35}{a\left(a+3\right)\left(a+6\right)}$$

Do the multiplications in 5aa\left(a+6\right)+\left(a+b\right)\times 35.

$$\frac{5a^{3}+30a^{2}+35a+35b}{a\left(a+3\right)\left(a+6\right)}$$

Expand a\left(a+3\right)\left(a+6\right).

$$\frac{5a^{3}+30a^{2}+35a+35b}{a^{3}+9a^{2}+18a}$$

Expand

$$\frac{5\left(a^{3}+6a^{2}+7a+7b\right)}{\left(a+3\right)\left(a^{2}+6a\right)}$$

Short Solution Steps

Multiply \frac{a+b}{a+3} times \frac{35}{a^{2}+6a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5a}{a+3}+\frac{\left(a+b\right)\times 35}{\left(a+3\right)\left(a^{2}+6a\right)}$$

Factor \left(a+3\right)\left(a^{2}+6a\right).

$$\frac{5a}{a+3}+\frac{\left(a+b\right)\times 35}{a\left(a+3\right)\left(a+6\right)}$$

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

$$\frac{5aa\left(a+6\right)}{a\left(a+3\right)\left(a+6\right)}+\frac{\left(a+b\right)\times 35}{a\left(a+3\right)\left(a+6\right)}$$

Since \frac{5aa\left(a+6\right)}{a\left(a+3\right)\left(a+6\right)} and \frac{\left(a+b\right)\times 35}{a\left(a+3\right)\left(a+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{5aa\left(a+6\right)+\left(a+b\right)\times 35}{a\left(a+3\right)\left(a+6\right)}$$

Do the multiplications in 5aa\left(a+6\right)+\left(a+b\right)\times 35.

$$\frac{5a^{3}+30a^{2}+35a+35b}{a\left(a+3\right)\left(a+6\right)}$$

Expand a\left(a+3\right)\left(a+6\right).

$$\frac{5a^{3}+30a^{2}+35a+35b}{a^{3}+9a^{2}+18a}$$