do the operation and simplify:?

Question

a+3/64- a^2 *2a - 16/2a + 6

Answer 1

I think you need some parentheses to clarify, but I'll assume these are two fractions you are multiplying:

a + 3 ..... 2a - 16
---------- x ----------
64 - a² ... 2a + 6

First I would do some factoring:

a + 3 ..... 2(a - 8)
---------- x ----------
64 - a² ... 2(a + 3)

You can cancel out the 2 from top and bottom, and the (a + 3):

(a - 8)
---------
64 - a²

If we multiply the numerator and denominator by -1, we can get the denominator in the same order as the numerator:

-(a - 8)
----------
-(64 - a²)

-(a - 8)
----------
a² - 64

Now the denominator is a difference of squares:

-(a - 8)
----------------
(a - 8)(a + 8)

Cancel out the (a - 8) and you have:
. -1
-------
a + 8

Answer 2

a+3/64- a^2 *2a - 16/2a + 6=2a^3+a+387/64-16/2a

Answer 3

[(a+3)/(64- a^2)] [(2a - 16)/(2a + 6)]

[(a + 3)/(8 + a)(8 - a)][2(a - 8)/2(a + 3)]

(a - 8)/(8 + a)(8 - a)

-(8 - a)/(8 + a)(8 - a)

-1/(a + 8)