I do not how to do this problem could some one help me please.
x+1/x+2-x^2+1/x^2-x-6
You will have to re-type it using brackets to establish the proper order of operations.
The way it stands it means
x + (1/x) - x^2 + (1/x^2) - x - 6
I am sure that is not what you meant
could it be
(x+1)/(x+2-x^2) + 1/(x^2-x-6) ?
x+1 over x+2 minus x^2+1 over x^2 minus x- minus 6
this is the right way
ok, I read that as
(x+1)/(x+2) - (x^2 + 1)/(x^2 - x - 6)
= (x+1)/(x+2) - (x^2 + 1)/[(x-3)(x+2)]
(so the LCD is (x-3)(x+2) )
= (x+1)(x+2)/[(x-3)(x+2)] - (x^2 + 1)/[(x-3)(x+2)]
= (x^2 + 3x + 2 - x^2 - 1)/[(x-3)(x+2)]
= (3x-1)/[(x-3)(x+2)]
To simplify the expression, we need to first find the common denominator for all the fractions involved.
Let's break down the denominator of the fractions:
x + 1 / x + 2 - x^2 + 1 / x^2 - x - 6
To find the common denominator, we need to factorize the denominators and determine the least common multiple:
The first denominator (x + 2) cannot be further simplified.
The second denominator (x^2 - x - 6) can be factored as (x - 3) (x + 2).
Now, let's rewrite the expression with the common denominator:
(x(x - 3)) / (x + 2) - ((x + 1)(x - 3)) / (x^2 - x - 6)
Since (x + 2) is the common denominator, we can combine the two fractions:
(x(x - 3) - (x + 1)(x - 3)) / (x + 2)
Now, we can simplify the numerator:
(x^2 - 3x - x^2 + 4x + 3) / (x + 2)
Combining like terms:
(x - x^2 + x + 3) / (x + 2)
Simplifying further:
(-x^2 + 2x + 3) / (x + 2)
Thus, the simplified expression is (-x^2 + 2x + 3) / (x + 2).