written wrong the first time...

[(x^2 -16) / (2x^2-9x + 4)] / [(2x^2 + 14x + 24) / (4x + 4)]

Is the answer?
1 / (3+1)

(x+4)(x-4) / (2x-1)(x-4) * 4(x+1) / 2(x+3)(x+4)

the x-4 and x+4 cancel, and we are left with

2(x+1) / (2x-1)(x+3)

where are all the x's in your answer?

next time you post this problem (again), why not show your work, so we can see what's giving you trouble?

Thank you, I will. that will help me learn.

To simplify the expression [(x^2 - 16) / (2x^2 - 9x + 4)] / [(2x^2 + 14x + 24) / (4x + 4)], we follow these steps:

Step 1: Factorize the polynomials if possible.
In this case, we notice that both the numerator and denominator of each fraction can be factored. Let's factorize them:

Numerator of the first fraction: (x^2 - 16)
This is a difference of squares, so we can factor it as follows: (x - 4)(x + 4).

Denominator of the first fraction: (2x^2 - 9x + 4)
This trinomial can be factored into two binomials: (2x - 1)(x - 4).

Numerator of the second fraction: (2x^2 + 14x + 24)
This trinomial can be factored into two binomials: 2(x + 2)(x + 6).

Denominator of the second fraction: (4x + 4)
This can be factored out a common factor of 4: 4(x + 1).

After factoring, the expression becomes:
[(x - 4)(x + 4) / (2x - 1)(x - 4)] / [2(x + 2)(x + 6) / 4(x + 1)]

Step 2: Simplify further.
To simplify a division of fractions, we invert the second fraction and multiply. So, let's rewrite the expression:

[(x - 4)(x + 4) / (2x - 1)(x - 4)] * [4(x + 1) / 2(x + 2)(x + 6)]

Step 3: Cancel out common factors.
The (x - 4) terms in the numerator and denominator can be canceled out, leaving us with:

[(x + 4) / (2x - 1)] * [4(x + 1) / 2(x + 2)(x + 6)]

Step 4: Multiply the numerators and denominators.
Multiplying the numerators and denominators together gives us:

4(x + 4)(x + 1) / 2(x - 1)(x + 2)(x + 6)

Step 5: Expand and combine like terms if necessary.
Expanding the numerator results in:

4(x^2 + 5x + 4)(x + 1)

And the denominator remains:

2(x - 1)(x + 2)(x + 6)

Step 6: Simplify the expression if possible.
To simplify further, we would need more information about the expression. Without specific values for 'x', we cannot simplify it any further.

Therefore, the simplified expression is:
4(x^2 + 5x + 4)(x + 1) / 2(x - 1)(x + 2)(x + 6)