X^2-2x-15/x^2+x-12*2x^2-6x/x^3+3x^2
Brackets are absolutely essential here.
I am sure you meant
(x^2-2x-15)/(x^2+x-12)*(2x^2-6x)/(x^3+3x^2)
= (x-5)(x+3)/( (x+4)(x-3) ) * 2x(x-3)/( x^2(x+3))
= 2(x-5)/(x(x+4)) or (2x -10)/(x^2 + 4x) , x ≠ ±3,0
To simplify the given expression:
x^2 - 2x - 15
---------------- * (2x^2 - 6x)
x^2 + x - 12 x^3 + 3x^2
We'll break it down into smaller parts and simplify separately.
First, let's simplify the numerator.
The expression x^2 - 2x - 15 can be factored as (x - 5)(x + 3).
So, the numerator becomes (x - 5)(x + 3).
Now, let's simplify the denominator.
For the denominator x^2 + x - 12, it can be factored as (x + 4)(x - 3).
The denominator becomes (x + 4)(x - 3).
Next, let's simplify the second part of the expression, (2x^2 - 6x).
We can factor 2x out from each term:
2x(x - 3)
Now, let's simplify the denominator of the second part, x^3 + 3x^2.
We can pull out an x^2 common factor:
x^2(x + 3)
Now, we can cancel out common factors between the numerator and denominator:
[(x - 5)(x + 3)] / [(x + 4)(x - 3)] * [2x(x - 3)] / [x^2(x + 3)]
Canceling common factors gives us:
(x - 5) / (x + 4) * 2 / x
Finally, we can simplify the expression further by multiplying:
2(x - 5) / (x + 4x)
This can be simplified to:
2x - 10 / x + 4x
or
(2x - 10) / (5x)
That's the simplified form of the given expression.