Simplify, stating any restrictions on the variables: x+1/2x^2-7x+6 - x-3/2x^2-x-3
assuming the usual carelessness with parentheses, I get
(x+1)/(2x^2-7x+6) - (x-3)/(2x^2-x-3)
= (x+1)/((x-2)(2x-3)) - (x-3)/((x+1)(2x-3))
Since division by zero is undefined, x=2, 3/2, -1 are excluded from the domain.
Combining over a common denominator yields
= ((x+1)^2 - (x-3)(x-2))/((x-2)(x+1)(2x-3))
= (7x-5)/((x-2)(x+1)(2x-3))
The three excluded values are still evident.
@ooblect are there any restrictions?
@oobleck
yes. I said which real numbers are excluded from the domain.
Uhhh .. those are restrictions, right?
To simplify the expression, we first need to combine like terms.
The given expression is: x + (1/2)x^2 - 7x + 6 - x - (3/2)x^2 - x - 3.
Grouping the like terms, we have: (x - x) + [(1/2)x^2 - (3/2)x^2] + (-7x - x) + (6 - 3).
Combining like terms within each group, we get: 0 + (-1/2)x^2 + (-8x) + 3.
Finally, arranging the terms in descending order of the exponent, we have: - (1/2)x^2 - 8x + 3.
So, simplifying the given expression results in -(1/2)x^2 - 8x + 3.
As for any restrictions on the variables, there are none specified in the given expression, so we can assume that x can take any real value.