Answer:
8x^2+8x
---------------------------------
(5x^2 -7x-6)
The restrictions are that any of the fractions cannot be zero
x≠2
x≠-1
x≠0
Explanation:
16/ (x-2)
----------------
4/(x+1) +6/x
The common denominator for all the fractions is (x-2)*(x+1)*x
So multiply by (x-2)(x+1)x over (x-2)(x+1)x
16/ (x-2) (x-2)(x+1)x
---------------- * -----------------
4/(x+1) +6/x (x-2)(x+1)x
16/ (x-2) * (x-2)(x+1)x
---------------------------------
4/(x+1) (x-2)(x+1)x + 6/x * (x-2)(x+1)x
Canceling terms
16 (x+1)x
---------------------------------
4 (x-2)x + 6 * (x-2)(x+1)
Distributing in the denominator
16 (x+1)x
---------------------------------
(4x^2 -8x) + 6 * (x^2-2x+x-2)
16 (x+1)x
---------------------------------
(4x^2 -8x) + (6x^2-6x-12)
16x^2+16x
---------------------------------
(10x^2 -14x-12)
Divide the top and bottom by 2
8x^2+8x
---------------------------------
(5x^2 -7x-6)
The restrictions are that any of the fractions cannot be zero
x-2 ≠0
x≠2
x+1≠0
x≠-1
x≠0