Question

How do you subtract `\frac { 6} { 13a } - \frac { 4} { 13a ^ { 2} }`?

Answer 1

`(6a-4)/(13a^2)`

Explanation:

In order to subtract two fractions, we need to find the lowest common multiple of their denominators.

For `13a` and `13a^2`, the lowest common multiple is `13a^2`.

So we need to multiply `6/(13a) xx a/a=(6a)/(13a^2)`.

We can now subtract the two fractions.

`(6a)/(13a^2)-4/(13a^2)=(6a-4)/(13a^2)`

Answer 2

See the entire solution process below:

Explanation:

To be able to add or subtract fractions they must be over common denominators. To put the fraction on the left in the expression over a common denominator we need to multiply it by the appropriate form of `1`, which will not change it's value. In this case we need to multiply it by `color(red)(a/a)`:

`6/(13a) - 4/(13a^2) = [color(red)(a/a) xx 6/(13a)] - 4/(13a^2) =`

`(6a)/(13a^2) - 4/(13a^2)`

We can now subtract the numerators over the common denominator:

`(6a - 4)/(13a^2)`

Answer 3

`\frac{6a}{13a^2}-\frac{4}{13a^2} = \frac{6a-4}{13a^2}`

Explanation:

Multiply the numerator and the denominator of the first fraction by `a` you will get:
`\frac{6a}{13a^2}-\frac{4}{13a^2} = \frac{6a-4}{13a^2}`

You might ask yourself how we could multiply the numerator and the denominator of a fraction by a number, doesn't that changes the answer?
The answer is no, it does not change the answer thus `\frac{a}{a}` is equal to one, and we just multiplied a number by one and the value won't change.