Problem 2:
(x+2)/(2x^2+5x+2) - (x-3)/(2x^2-5x-3)
What I did:
2x^2+5x+2 factors are (2x+1)(x+2)
2x^2-5x-3 factors are (2x+1)(x-3)
Then:
(x+2)/(2x+1)(x+2) - (x-3)/(2x+1)x-3)
So the common denominator is
(2x+1)(x+2)(x-3)
using that combine the fractions.
I already knew the common denominator.I wanted to see if my work was correct.Do I need to simplify more or what?
Your work in finding the factors of both denominators is correct. However, your simplification is not yet complete.
To add or subtract fractions, you need a common denominator. In this case, the common denominator is (2x + 1)(x + 2)(x - 3), which you correctly identified.
Now, let's simplify further. The first fraction, (x + 2)/(2x + 1)(x + 2), can be written as 1/(2x + 1) since (x + 2) cancels out. Similarly, the second fraction, (x - 3)/(2x + 1)(x - 3), can be written as 1/(2x + 1) since (x - 3) cancels out.
So, our expression becomes:
1/(2x + 1) - 1/(2x + 1)
Now, we can combine the fractions since they have the same denominator:
(1 - 1)/(2x + 1)
Simplifying further:
0/(2x + 1)
The final result is 0.