ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH UNLIKE DENOMINATOR

There are two methods to add or subtract rational expressions with unlike denominators.

  1. Least common multiple
  2. Cross multiplication

Method 1 : (Using Least common multiple)

Step 1 :

If the given two or more rational expressions to added or subtracted with unlike denominators, we will use the Least Common Multiple(LCM).

Step 2 :

To get the result, simplify the numerator and denominator if needed.

Method 2 : (Using cross multiplication)

Step 1 :

If the given two rational expressions to added or subtracted with unlike denominators, we will use the cross multiplication.

Step 2 :

To get the result, simplify the numerator and denominator if needed.

Note :

Sometimes there must be a necessity of using algebraic identities and factorization.

Problem 1 :

Solution :

The denominators are almost same, using the negative sign in the middle, we get

Problem 2 :

Solution :

(a-4) and (4-a) both are almost same.

By factoring the negative sign from (4-a), we get -(4-a).

Problem 3 :

Solution :

Since the denominators are not the same, we are using cross multiplication.

Problem 4 :

Solution :

Since the denominators are not the same, we are using the cross multiplication.

Problem 5 :

Solution :

Since the denominators are not the same, we are taking the common factor of 2b + 6, we get

Problem 6 :

Solution :

Problem 7 :

Solution :

Problem 8 :

Solution :

Problem 9 :

Solution :

Since the denominators are not the same, we are using the least common multiple.

Problem 10 :

Solution :

By factoring the denominators, we get

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