Final answer:
To multiply the given rational expressions, we need to first factorize both the numerators and denominators and then cancel out any common factors.
Step-by-step explanation:
To multiply the given rational expressions: (2-5x-3x²)/(4-x²)*(x²-x-2)/(9x²-1), we need to first factorize both the numerators and denominators and then cancel out any common factors.
Factoring the first numerator, we get: (2-5x-3x²) = -(3x+2)(x-1)
Factoring the second numerator, we get: (x²-x-2) = (x-2)(x+1)
Factoring the first denominator, we get: (4-x²) = (2-x)(2+x)
Factoring the second denominator, we get: (9x²-1) = (3x-1)(3x+1)
Now, we can cancel out the common factors:
(-1)(3x+2)(x-2)(x+1) / (2-x)(2+x)(3x-1)(3x+1)
So, the correct result of the multiplication is (-1)(3x+2)(x-2)(x+1) / (2-x)(2+x)(3x-1)(3x+1)