# Denominators with no common factorsGive example

hala718 | Certified Educator

When we need to do an operation on two rational numbers, first we need to have a common denominator.

If the ddenominators are not the same, then we will have to multiply the denominators by each other in order to have a common denominator.

For example:

3/(x-1) + 2x/(x-3)

We notice that the denominators are different.

==> (3(x-3)/(x-1)(x-3)  + 2x(x-1)/(x-1)(x-3)

Now we have the same denominator, then we will add the numerators.

==> (3x-9)+(2x^2-2x)/(x-1)(x-3)

==> (2x^2+x-9)/(x^2-4x+3)

justaguide | Certified Educator

The number of prime numbers is infinite, so is the number of sets of co-prime numbers. Whenever the denominators are co-prime, they have no common factor except 1.

Some examples of denominators that have no common factors have been given above, you can frame an infinite number of such examples.

opopopopoq | Student

Is there an infinate # of them or limited?

giorgiana1976 | Student

Let's  have an example:

2/(x-1) + 1/x

We notice that the denominators are not the same.

We'll have to calculate the LCD (least common denominator)

LCD = x(x-1)

We'll multiply by LCD both fractions:

2x(x-1)/(x-1) +  x(x-1)/x

Since the fractions have the same denominator, we can add them:

(2x + x - 1)/x(x-1) = (3x-1)/x(x-1)