(4x+6)/(16x^2-36)/(4x^2+22x-42)
To simplify the expression (4x+6)/(16x^2-36)/(4x^2+22x-42), we can follow the order of operations and simplify step by step.
Step 1: Simplify the individual expressions in the numerator and denominator.
The numerator is 4x + 6.
The denominator has two terms: 16x^2 - 36 and 4x^2 + 22x - 42.
The numerator does not factor further.
The denominator terms can be factored:
16x^2 - 36 can be factored as 4(4x^2 - 9), and
4x^2 + 22x - 42 can be factored as (2x + 7)(2x - 3).
Step 2: Rewrite the expression with the factored terms.
So, our expression becomes:
(4x + 6) / (4(4x^2 - 9)) / ((2x + 7)(2x - 3))
Step 3: Simplify further by canceling out common factors.
In the numerator, we can see a common factor of 2 in both the 4x and the 6. So, we can rewrite the numerator as 2(2x + 3).
In the denominator, the 4 in the factor 4(4x^2 - 9) can be canceled out with the 4 in the numerator. Also, the (2x - 3) in the denominator can be canceled out with the (2x - 3) in the numerator.
After canceling out the common factors, our expression becomes:
2(2x + 3) / (4x^2 - 9)(2x + 7)
This is the simplified form of the given expression.
Therefore, the simplified expression is: 2(2x + 3) / (4x^2 - 9)(2x + 7)