Rational Expression

In arithmetic we combine fractions with different denominators by finding a common denominator which becomes the new denominator. The new denominator is divided by the old denominator and the answer multiplied by the old numerator. This new number becomes the new numerator over the new denominator.
A common denominator is a number that can be divided by the other denominators and the answer will not have a remainder.
For instance 12, 24, 36 and a number of other numbers are common denominators of 4 and 12 but 12 is the smallest common denominator.

Why can a number be divided by another number and not leave a remainder?  answer

Fractions are treated the same way in algebra. We need to find a common denominator and then divide this new denominator by the old denominator.

The answer from this division is multiplied by the old numerator and we obtain the new numerator.
For example cxy ÷ x = cy  cy multiplied by a = acy.  This is the new numerator.

Next we add the numerators together and bring over the common denominator.

Try these examples:

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