Question

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

Answer 1

`11a-2/(5a)`

Explanation:

`12a-7/(35a)-a-1/(5a)` actually contains two different variables:

`a` and `1/a`.

`12a-7/(35a)-a-1/(5a)`

`=12a-a-7/(35a)-[1(7)]/[(5a)(7)]`

`=11a-7/(35a)-7/(35a)`

`=11a-14/(35a)`

`=11a-2/(5a)`

Answer 2

convert to whole numbers and then combine.

Explanation:

`7/(35a)` can be simplified to `1/(5a)` then we have another `1/(5a)` so we add those 2 and deal with the whole number separately. Thus we get `12a- a - 1/(5a) - 1/(5a) = 11a - 2/(5a)`.

Answer 3

`=(55a^2-a-2)/(5a)`

Explanation:

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

`12a-7/(35a) -a-1/(5a)" "larr LCD = 35a`

The `LCD = 35a`

`=(12a)/1 xx(35a)/(35a)-7/(35a) -a/1xx(35a)/(35a)-1/(5a) xx7/7`

`= (420a^2)/(35a) -7/(35a)-(35a^2)/(35a)-(7)/(35a)`

`=(420a^2 -7-35a^2 -7)/(35a)`

`=(385a^2-7a-14)/(35a)`

There is common factor of `7`

`=(cancel7(55a^2-a-2))/(cancel35^5a)`

`=(55a^2-a-2)/(5a)`

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

`12a-cancel7/(cancel35^5a) -a-1/(5a)" "larr LCD = 5a`

`=(12a)/1-1/(5a) -a/1-1/(5a)`

`= (60a^2 -1-5a^2-1)/(5a)`

`=(55a^2-a-2)/(5a)`