# If 3 is added to the number and denominator of a fraction and the result subtracted 'by' the original fraction, the difference is 1/15. The numerator of the original fraction is 6 less than the denominator. What is the original fraction?

##### 1 Answer

#### Explanation:

So if the original fraction's numerator is

Then, the second fraction is

We are also told the the difference between the second fraction and the first fraction is

Now, we have to find the LCD to be able to work with fractions with different denominators. The LCD in this case would be

Let's distribute the

Then distribute the

Now, we can expand both sides to get:

Now, if we move all the terms to one side and do some simplification, we get:

If we multiply both sides by

Factoring, we get:

Thus, the solutions for x are

Quickly checking the first expression, you get