simplify ((x - 5)(x + 1))/(8x ^ 2 * (x + 3)) * (2(x + 6))/((x + 6)(5 - x)) * (x ^ 3 * (x + 3))/(x + 1)
To simplify the expression, we can cancel out common factors in the numerator and denominator.
We have:
((x - 5)(x + 1))/(8x ^ 2 * (x + 3)) * (2(x + 6))/((x + 6)(5 - x)) * (x ^ 3 * (x + 3))/(x + 1)
Let's start by canceling out common factors:
Cancel out (x + 1) in the numerator and denominator:
((x - 5) * 1)/(8x ^ 2 * (x + 3)) * (2(x + 6))/((x + 6)(5 - x)) * (x ^ 3 * (x + 3))/1
The (x + 1) terms are canceled out, and we're left with:
(x - 5)/(8x ^ 2 * (x + 3)) * (2(x + 6))/((x + 6)(5 - x)) * (x ^ 3 * (x + 3))/1
Now, we can simplify further:
(x - 5)(2(x + 6))(x ^ 3 * (x + 3))/(8x ^ 2 * (x + 3) * (x + 6)(5 - x))
Combining like terms:
(2(x - 5))(x ^ 3 * (x + 3))/(8x ^ 2 * (x + 3) * (x + 6)(5 - x))
The simplified expression is:
(2(x - 5)x ^ 3 * (x + 3))/(8x ^ 2 * (x + 3) * (x + 6)(5 - x))