Final answer:
To multiply the given rational expressions, we cancel out common factors and then multiply the numerators and denominators separately. The final simplified expression is (2x⁴ - x³ - 7x² + 4x) / (x+1).
Step-by-step explanation:
To multiply the rational expressions (2x²-9x+4)/(x+1)*(x²-1)/(2x²-9x+4), we can cancel out common factors to simplify the expression. In this case, the expression (2x²-9x+4)/(2x²-9x+4) can be simplified to 1, since any number divided by itself is equal to 1. Therefore, the expression simplifies to (2x²-9x+4)/(x+1) * (x²-1)/1. To multiply the rational expressions, we multiply the numerators and denominators separately, then simplify the resulting expression:
- (2x²-9x+4) * (x²-1) = 2x⁴ - x³ - 7x² + 4x
- (x+1) * 1 = x+1
Therefore, the final simplified expression is:
(2x⁴ - x³ - 7x² + 4x) / (x+1)