Math

Adding and Subtracting Rational Expressions

CASE 1) Adding and Subtracting Rational Expressions with Common Variable Denominators: in this case, we only need to add/subtract the numerators.

Example: Subtract

We only need to subtract the numerators:

CASE 2) Adding and Subtracting Rational Expressions with Unlike Variable Denominators: in this case, we find a common denominator first and then proceed with the addition or subtraction.

Example: Add

To add these rational expressions, we need to find their common denominator. Since the denominators have nothing in common their common denominator is equal to their product:.

So, we multiply the first fraction by and multiply the second fraction by:

We then expand the numerators of each expression and add them together:

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