a+b/a-b + a²-4b²/a²-b² - a-3b/a+b
How to solve this question and how to take the LCM of followings?.
do you mean?
(a+b)/(a-b)
+ (a-2b)(a+2b)/[(a-b)(a+b)]
- (a-3b)/(a+b)
if so then
(a+b)^2/[(a-b)(a+b)]
+ (a-2b)(a+2b)/[(a-b)(a+b)]
- (a-3b)(a-b)/[(a-b)(a+b)]
[ a^2 + 2 a b + b^2 + a^2-4b^2 -a^2 -4 ab + 3b^2]/ [(a-b)(a+b)]
= [a^2 -2ab ]/[(a-b)(a+b)]
= a (a-2b)/(a^2-b^2)
check arithmetic !
To solve the given expression, you need to find the Least Common Multiple (LCM) of the denominators and then simplify the expression using the LCM.
Step 1: Factorize the denominators:
- For (a - b), no further factorization is possible.
- For (a^2 - 4b^2), we can rewrite it as (a - 2b)(a + 2b) using the difference of squares formula.
- For (a^2 - b^2), we can rewrite it as (a - b)(a + b) using the difference of squares formula.
- For (a + b), no further factorization is possible.
- For (a + 3b), no further factorization is possible.
Step 2: Find the LCM of the denominators:
The LCM of the denominators is the product of unique prime factors raised to their highest powers. In this case, the LCM is (a - b)(a + 2b)(a + b)(a + 3b).
Step 3: Simplify the expression:
Multiply each term in the expression by the LCM of the denominators. This will clear out the denominators, allowing us to simplify the expression.
a+b/a-b + a²-4b²/a²-b² - a-3b/a+b
= (a + b)(a - b)(a + 2b)(a + b)(a + 3b) / [(a - b)(a + 2b)(a + b)(a + 3b)]
Here, we can cancel out the common factors:
= (a + b)(a - b)(a + 3b) / (a - b)(a + 2b)(a + 3b)
The simplified expression is:
= (a + b)(a + 3b) / (a + 2b)
So, the simplified expression is (a + b)(a + 3b) / (a + 2b).
By following these steps, you can solve the given expression and find the LCM of the denominators.