[15 points, algebra 2]simplify the complex fraction and find the restrictions.

8x^2+8x

(5x^2 -7x-6)    

The restrictions are that any of the fractions cannot be zero

x≠2

x≠-1

x≠0

Step-by-step 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

the first option is the answer.

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step-by-step explanation: