(16/(x-2))/(4/(x+1)+6/x) Simplify the complex fraction.

To simplify the given complex fraction (16/(x-2))/(4/(x+1)+6/x) , we may look for the LCD or least common denominator.
The denominators are (x-2) , x , and (x+1) . All are distinct factors.
Thus, we get the LCD by getting the product of the distinct factors from denominator side of each term.
LCD =(x-2)*x* (x+1)
Maintain the factored form of the LCD for easier cancellation of common factors on each term.
Multiply each term by the LCD=(x-2)*x* (x+1).
(16/(x-2)*(x-2)*x* (x+1))/(4/(x+1)*(x-2)*x* (x+1)+6/x*(x-2)*x* (x+1))
(16*x* (x+1))/(4*(x-2)*x +6*(x-2)* (x+1))
Apply distributive property.
(16x*(x+1))/((4x-8)*x +(6x-12)* (x+1))
(16x^2+16x)/((4x^2-8x) +(6x^2+6x-12x-12))
Combine possible like terms.
(16x^2+16x)/((4x^2-8x) +(6x^2-6x-12))
(16x^2+16x)/(4x^2-8x+6x^2-6x-12)
(16x^2+16x)/(10x^2-14x-12)
Factor out 2 from each side.
(2(8x^2+8x))/(2(5x^2-7x-6))
Cancel out common factor 2 .
(8x^2+8x)/(5x^2-7x-6)
 The complex fraction (16/(x-2))/(4/(x+1)+6/x) simplifies to (8x^2+8x)/(5x^2-7x-6) .