x cubed + x squared over x squared - 16 times x + 4 over 3x to the fourth power + x cubed - 2x squared.
i got x + 1 over (x-4) (x+1) (3x+2).
is this correct?
now cancel your x+1 and you got it...
actually I got over 1/(x-4)(3x-2)...slightly different.
oh. i re-did the problem and got that- i got the signs confused and forgot to cancel the x+1 before... thanks
To simplify the given expression, let's break it down step by step:
1. First, let's simplify the numerator and denominator separately.
Numerator: x^3 + x^2
Denominator: x^2 - 16
2. The numerator can be factored by taking out the common factor x^2:
Numerator: x^2(x + 1)
3. Similarly, the denominator is a difference of squares, so it can be factored:
Denominator: (x - 4)(x + 4)
4. Next, let's simplify the second part of the expression:
(x + 4) / (3x^4 + x^3 - 2x^2)
5. For this part, it is advisable to factor out the highest common factor, which in this case is x^2:
(x + 4) / (x^2(3x^2 + x - 2))
6. Now, let's factor the quadratic expression:
(x + 4) / (x^2(3x^2 + 3x - 2x - 2))
7. Continuing to factor, we have:
(x + 4) / (x^2(x(3x + 3) - 2(3x + 1)))
8. Further simplifying:
(x + 4) / (x^2(x(3x + 3) - 2(3x + 1)))
9. Combining like terms:
(x + 4) / (x^2(x(3x + 3) - 6x - 2))
10. Simplifying:
(x + 4) / (x^2(3x^2 + 3x - 6x - 2))
11. Continuing to simplify:
(x + 4) / (x^2(3x^2 - 3x - 2))
Therefore, the simplified expression is:
(x^2(x + 1)(x + 4)) / (x^2(x - 4)(3x^2 - 3x - 2))
So, the expression you got, x + 1 / (x - 4)(x + 1)(3x + 2), is not correct.