Quick adding and subtracting algebraic fractions summary
This quick entry summaries the techniques used in subtracting and adding algebraic fractions. Below are some examples;
Fractions denominator common multiple
In the following examples we shall explore how to find the common denominator of fractions before adding or subtracting. In most cases you will have to find the common multiple of the denominators before adding or subtracting;
Example
Here is an example; Suppose we had to add the following fractions;
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First we find the lowest common multiple of the two denominators since the two numbers are not equal; The lowest common multiple of 3 and 4 is 12. Since we’re trying to change the denominators to a higher number that must mean that the numerators will change to keep the ratio of the fractions equal or the same. To make the denominator of the first fraction 12 we multiply by 4, therefore we must also multiply the numerator by 4 i.e;
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For the next fraction 2/4 we must do the same. To make the denominator 12 we must multiply it by 3 to keep it the same as before, i.e;
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So we have the expression;
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Now it is easy to work out the expression, we simply add the two numerators together to get;
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Notice that we can simplify the fraction further because;
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Example
In this algebraic example we shall work with subtraction, the same principle applies whether subtraction or addition. In this example we shall work out;
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We must find the lowest common multiple of the two denominators because they are not equal. To find the lowest common multiple of the denominators we multiply them together. The lowest common multiple here is (x+3)(x+1). Remember what we do to the numerator we do to the denominator; to make the first fraction denominator equal to (x+3)(x+1) we must multiply it by (x+1) i.e;
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The same applies to the second fraction to make the denominator equal to the lowest common multiple we must multiply it by (x+3) and do the same to the numerator;
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So we have the full expression;
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We simply just subtract the numerators since the denominators are similar;
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…and that is it.
