x+3 over x cubed - x squared -6x divided by x squared -9 over x squared + x -12.
i got x + 4 over (x squared + 2x)(x-3).
am i right?
you are right!
thanks
To determine if your answer is correct, we can simplify both the numerator and denominator separately and then divide them.
Let's start by simplifying the numerator:
The numerator is (x + 3)/ (x^3 - x^2 - 6x).
We can factor out an x from the denominator and rewrite it as:
(x + 3)/ (x(x^2 - x - 6)).
Factorizing the quadratic term (x^2 - x - 6), we get (x - 3)(x + 2), so the denominator becomes:
(x + 3)/ (x(x - 3)(x + 2)).
Next, let's simplify the denominator:
The denominator is (x^2 - 9)/ (x^2 + x - 12).
We can factorize (x^2 - 9) as (x - 3)(x + 3), so the denominator becomes:
(x - 3)(x + 3)/ (x^2 + x - 12).
Now, when we divide the numerators and denominators, we invert the second fraction and multiply:
[(x + 3)/ (x(x - 3)(x + 2))] * [(x^2 + x - 12)/ (x - 3)(x + 3)]
Note that (x - 3) and (x + 3) cancel out in both the numerator and the denominator:
x + 3/ (x(x + 2)) * (x^2 + x - 12)/ 1
Simplifying further:
(x + 3)(x^2 + x - 12)/ x(x + 2)
Now, let's multiply the terms in the numerator:
x^3 + x^2 - 12x + 3x^2 + 3x - 36/ x(x + 2)
Combining like terms:
x^3 + 4x^2 - 9x - 36/ x(x + 2)
Hence, your answer should be x^3 + 4x^2 - 9x - 36/ x(x + 2), not x + 4/ (x^2 + 2x)(x - 3).