what is (x to the 3rd power + x to the 2nd power) divided by ((x+4)(X-4)) multiplied by (x+4) divided by (3x to the 4th power + x to the 3rd power + 2x to the 2nd power)
Is this what you like simplified?
(x³ + x²)/((x+4)(x-4)) * (x+4)/(3x4 + x³ + 2x²)
Hint:
Cancel the common factor (x+4).
The second denominator can be factored into x²(3x²+x+2)
help me
To simplify the given expression, let's break it down step by step:
1. (x^3 + x^2) / [(x+4)(x-4)] * (x+4) / (3x^4 + x^3 + 2x^2)
2. Let's start by factoring the denominators:
The denominator (x+4)(x-4) can be expanded as (x^2 - 16).
3. Now, the expression becomes:
(x^3 + x^2) / (x^2 - 16) * (x+4) / (3x^4 + x^3 + 2x^2)
4. Next, let's simplify the expression by canceling out any common factors:
The numerator (x^3 + x^2) does not have any common factors with the denominators, so we cannot cancel anything out in the numerator.
5. For the denominator (x^2 - 16), we can use the difference of squares identity to rewrite it as (x + 4)(x - 4).
6. The expression now becomes:
(x^3 + x^2) / [(x + 4)(x - 4)] * (x + 4) / (3x^4 + x^3 + 2x^2)
7. Next, we cancel out common factors between the numerator and denominator:
(x + 4) in the numerator and denominator can be canceled out.
8. The expression simplifies to:
(x^3 + x^2) / (x - 4) * (1) / (3x^4 + x^3 + 2x^2)
9. Finally, we have:
(x^3 + x^2) / (x - 4) / (3x^4 + x^3 + 2x^2)
And that is the simplified expression.