Answer:
[x(x - 1)(x - 4)]/(2(x + 4))
Step-by-step explanation:
We want to find;
[(x² - 16)/(2x + 8)] * [(x³ - 2x² + x)/(x² + 3x - 4)]
Now,
x² - 16 can be factorized as;
(x + 4)(x - 4)
Also, 2x + 8 can be factorized as;
2(x + 4)
Also, (x³ - 2x² + x) can factorized as;
x[x² - 2x + 1] = x[(x - 1)(x - 1)]
Also,(x² + 3x - 4) can be factorized out as; (x - 1)(x + 4)
So plugging in these factorized forms into the equation in the question, we have;
[(x + 4)(x - 4)/(2(x + 4))] * [x[(x - 1)(x - 1)] /((x - 1)(x + 4))
This gives;
((x - 4)/2) * x(x - 1)/(x +4)
This gives;
[x(x - 1)(x - 4)]/(2(x + 4))
