Problem 1:
(x-2)/(3x+4) - 6x/(x+1)
What I did:
Common denominator is: (3x+4)(x+1)
(x-2)(x+1)/(3x+4)(x+1) - 6x(3x+4)/(x+1)(3x+4)
[(x-2)(x+1) - 6x(3x+4)] / (x+1)(3x+4)
(x^2 - x - 2 - 18x^2 - 24x) / (x+1)(3x+4)
x^2 - 18x^2 = -17x^2
-x - 24x = -25x
(-17x^2 - 25x - 2) / (x+1)(3x+4)
I don't see any errors.
The steps you have taken so far are correct. You found the common denominator, which is (3x+4)(x+1), and then combined the fractions using the common denominator. However, there is a small error in your final expression.
Let's go over the steps again:
1. Find the common denominator: (3x+4)(x+1).
2. Rewrite the given fractions using the common denominator:
(x-2)/(3x+4) - (6x)/(x+1).
3. Combine the fractions:
((x-2)(x+1) - 6x(3x+4))/((x+1)(3x+4)).
4. Simplify the expression:
(x^2 - x - 2 - 18x^2 - 24x)/((x+1)(3x+4)).
5. Combine like terms:
(-17x^2 - 25x - 2)/((x+1)(3x+4)).
So, the correct expression for the given problem is:
(-17x^2 - 25x - 2)/((x+1)(3x+4)).