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Multiply the following rational expressions: (2-5x-3x²)/(4-x²)*(x²-x-2)/(9x²-1). What is the correct result of the multiplication?

User Mph
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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)

User Apb
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