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