((3-2x)/x^3)/(2/x^2-1/(x^3+x^2)) Simplify the complex fraction.

To simplify the given complex fraction ((3-2x)/x^3)/(2/x^2-1/(x^3+x^2)) , we may look for the LCD or least common denominator.
The denominators are x^3 , x^2, andx^3+x^2 .
Note: The factored form of x^3+x^2 = x^2(x+1).
LCD is the same as getting LCM from the denominators.
We get the product of each factor with highest exponent value,
LCD=x^3*(x+1) .
Multiply each term by the LCD=x^3*(x+1).
((3-2x)/x^3*x^3*(x+1))/(2/x^2*x^3*(x+1)-1/(x^3+x^2)x^3*(x+1))
((3-2x)/x^3*x^3*(x+1))/(2/x^2*x^3*(x+1)-1/(x^2(x+1))x^3*(x+1))
((3-2x)(x+1))/(2x*(x+1)-1*x)
(3x+3-2x^2-2x)/((2x^2+2x)-x)
(-2x^2+3x-2x+3)/(2x^2+2x-x)
(-2x^2+x+3)/(2x^2+x)
Final answer:
((3-2x)/x^3)/(2/x^2-1/(x^3+x^2))=(-2x^2+x+3)/(2x^2+x)