# How do you combine 12a - 7/(35a) - a - 1/(5a)?

Mar 4, 2018

$11 a - \frac{2}{5 a}$

#### Explanation:

$12 a - \frac{7}{35 a} - a - \frac{1}{5 a}$ actually contains two different variables:

$a$ and $\frac{1}{a}$.

$12 a - \frac{7}{35 a} - a - \frac{1}{5 a}$

$= 12 a - a - \frac{7}{35 a} - \frac{1 \left(7\right)}{\left(5 a\right) \left(7\right)}$

$= 11 a - \frac{7}{35 a} - \frac{7}{35 a}$

$= 11 a - \frac{14}{35 a}$

$= 11 a - \frac{2}{5 a}$

Mar 4, 2018

convert to whole numbers and then combine.

#### Explanation:

$\frac{7}{35 a}$ can be simplified to $\frac{1}{5 a}$ then we have another $\frac{1}{5 a}$ so we add those 2 and deal with the whole number separately. Thus we get $12 a - a - \frac{1}{5 a} - \frac{1}{5 a} = 11 a - \frac{2}{5 a}$.

Mar 4, 2018

$= \frac{55 {a}^{2} - a - 2}{5 a}$

#### Explanation:

You have to add the fractions by finding a common denominator first and using the equivalent fractions.

$12 a - \frac{7}{35 a} - a - \frac{1}{5 a} \text{ } \leftarrow L C D = 35 a$

The $L C D = 35 a$

$= \frac{12 a}{1} \times \frac{35 a}{35 a} - \frac{7}{35 a} - \frac{a}{1} \times \frac{35 a}{35 a} - \frac{1}{5 a} \times \frac{7}{7}$

$= \frac{420 {a}^{2}}{35 a} - \frac{7}{35 a} - \frac{35 {a}^{2}}{35 a} - \frac{7}{35 a}$

$= \frac{420 {a}^{2} - 7 - 35 {a}^{2} - 7}{35 a}$

$= \frac{385 {a}^{2} - 7 a - 14}{35 a}$

There is common factor of $7$

$= \frac{\cancel{7} \left(55 {a}^{2} - a - 2\right)}{{\cancel{35}}^{5} a}$

$= \frac{55 {a}^{2} - a - 2}{5 a}$

Note that it would have been better to simplify right at the beginning!

$12 a - \frac{\cancel{7}}{{\cancel{35}}^{5} a} - a - \frac{1}{5 a} \text{ } \leftarrow L C D = 5 a$

$= \frac{12 a}{1} - \frac{1}{5 a} - \frac{a}{1} - \frac{1}{5 a}$

$= \frac{60 {a}^{2} - 1 - 5 {a}^{2} - 1}{5 a}$

$= \frac{55 {a}^{2} - a - 2}{5 a}$