Factorize x + 1/x - 1 + x + 3/x - 2 find the sum and products of the roots
To factorize x + 1/x - 1 + x + 3/x - 2, we first need to combine like terms:
x + 1/x - 1 + x + 3/x - 2
= 2x + 4/x - 3
Now, to factorize this expression, we need to find a common denominator which is x:
(2x^2 + 4 - 3x)/x
= (2x^2 - 3x + 4)/x
The roots of this expression can be found by setting the numerator equal to zero:
2x^2 - 3x + 4 = 0
Using the quadratic formula, we find that the roots are:
x = (3 ± sqrt(3^2 - 4(2)(4))) / 4(2)
x = (3 ± sqrt(9 - 32)) / 4
x = (3 ± sqrt(-23)) / 4
Since the square root of a negative number is not a real number, the roots of the expression are complex numbers, and the sum and product of the roots cannot be determined.