Answer:
Step-by-step explanation:
Rewrite x^2-16/2x+8 as
x^2 - 16
-------------
2(x + 8)
and rewrite x^3-2x^2+x/x^2+3x-4 as
x^3-2x^2+x
-----------------
x^2+3x-4
Next, write "x^2-16/2x+8 times x^3-2x^2+x/x^2+3x-4" as
x^2 - 16 x^3-2x^2+x
--------------- * -------------------
2(x+8) x^2+3x-4
Now factor both numerators and both denominators. We get:
(x - 4)(x + 4)(x)(x^2 - 2x + 1)
--------------------------------------
2(x + 8)(x + 4)(x - 1)
Now begin cancelling wherever possible. The x + 4 factors cancel, leaving us with:
(x - 4)(x)(x - 1)(x - 1)
---------------------------
2(x + 8)(x - 1)
Cancelling the x - 1 factors yields:
(x - 4)(x)(x - 1) x(x - 4)
--------------------- = -------------------
2(x + 8) 2(x + 8)
