problem 1.
(2x^2-5x+3)/(x^2-1)*(x^2+1)/(2x^2-x-3)
problem 2.
(n+3)/(2n^2-n-3)-(-n^2-3n)/(2n^2-n-3)
To solve problem 1, we will simplify the given expression step by step. Here's how:
1. Factorize both numerator and denominator.
(2x^2-5x+3) = (2x-3)(x-1)
(x^2-1) = (x-1)(x+1)
(x^2+1) = (x+i)(x-i) (where i is the imaginary unit)
(2x^2-x-3) = (2x+3)(x-1)
2. Cancel out common factors.
After factorization, we can cancel the common factors in both the numerator and denominator. In this case, the (x-1) term cancels out.
[(2x-3)(x-1)]/[(x-1)(x+1)] * [(x+i)(x-i)]/[(2x+3)(x-1)]
Simplified expression: (2x-3)(x+i)(x-i)/[(x+1)(2x+3)]
To solve problem 2, we will apply similar steps to simplify the given expression.
1. Factorize both numerator and denominator.
(n+3) does not factorize further.
(2n^2-n-3) = (2n+3)(n-1)
(-n^2-3n) = -(n+3)n
(2n^2-n-3) = (2n+3)(n-1)
2. Cancel out common factors.
After factorization, we can cancel the common factors in both the numerator and denominator. In this case, the (2n+3) term cancels out.
(n+3)/[(2n+3)(n-1)] - [-(n+3)n]/[(2n+3)(n-1)]
Simplified expression: (n+3 - n(n+3))/[(2n+3)(n-1)]
Please note that for both problems, we have simplified the expressions by factoring the terms and then canceling out the common factors in the numerator and denominator, thus reducing the complexity of the expression.