How to Add Rational Expressions with Different Denominators

Rational expressions are also known as algebraic expressions. A rational expression is the quotient of two polynomials. It is important to remember that the divisor cannot be zero. A quotient is the answer to a division problem. Polynomials are expressions with the sum of powers with at least one variable multiplied by coefficients.NOTE THAT ANY NUMBER AFTER A LETTER IS AN EXPONENT IN THE FOLLOWING ARTICLE: a2 IS A TO THE 2ND POWER FOR INSTANCE.

Instructions

How to Add Rational Expressions with Different Denominators

1. Original problem: 2/6a2+4/3aFirst, look for a common denominator. In this case, the common denominator is 6a2. The common denominator is found by finding the least common multiple (LCM). For instance, 3x1=3, 3x2=6; 6x1=6. 6 is the LCM between the numbers. Likewise, ax1=a, axa=a2. a2 is the LCM for the variables. Therefore, 6a2 is the LCM.2/6a2+4/3a=2 x 1/6a2 x 1=2/6a2 and 4 x 2a/3a x 2a=8a/6a2

2. Add or subtract the numerator. In this case, add the numerators.2/6a2+8a/6a2= 2+8a

3. Keep the common denominator as the denominator in the answer.2+8a/6a2

4. Simplify, if needed.2+8a/6a2=2(1+4a)/2(3a2)=1+4a/3a2Answer: 1+4a/3a2