3/x+1 - 1/x-2
No
To simplify the expression (3/x+1) - (1/x-2), we need to find a common denominator for the fractions.
The denominators of the two fractions are (x+1) and (x-2). To find a common denominator, we multiply these two denominators together.
Common denominator = (x+1) * (x-2)
Next, we need to adjust the numerators of the fractions to have the same denominator.
For the first fraction, we multiply both the numerator and denominator by (x-2):
(3 * (x-2)) / ((x+1) * (x-2))
For the second fraction, we multiply both the numerator and denominator by (x+1):
(1 * (x+1)) / ((x+1) * (x-2))
Now, our expression becomes:
(3(x-2) / ((x+1)(x-2))) - ((x+1) / ((x+1)(x-2)))
Next, we can combine the fractions:
((3x - 6) - (x+1)) / ((x+1)(x-2))
Now, we simplify the numerator:
(3x - 6 - x - 1) / ((x+1)(x-2))
Combining like terms in the numerator:
(2x - 7) / ((x+1)(x-2))
So, the simplified expression is (2x - 7) / ((x+1)(x-2)).
You probably meant: 3/(x+1) - 1/(x-2)
= (3(x-2) - 1(x+1))/((x+1)(x-2))
= (3x - 6 - x - 1)/(x^2 - x - 2)
= (2x - 7)/(x^2 - x - 2)
Is that what you wanted?