To determine the sum of the two given expressions, we need to follow these steps in the correct order:
1. Factor the denominators of each fraction:
[tex]\[
\frac{3(x+2)}{(x+2)(x-3)}+\frac{2 x}{(x-3)(x+4)}
\][/tex]
2. Simplify the first fraction by canceling the common factor in the numerator and the denominator:
[tex]\[
\frac{3}{(x-3)}+\frac{2 x}{(x-3)(x+4)}
\][/tex]
3. Rewrite the first fraction with the common denominator (x - 3)(x + 4):
[tex]\[
\frac{3(x+4)}{(x-3)(x+4)}+\frac{2 x}{(x-3)(x+4)}
\][/tex]
4. Combine the numerators over the common denominator:
[tex]\[
\frac{(3(x+4) + 2 x)}{(x-3)(x+4)}
\][/tex]
The correct order of steps is:
- [tex]\(\frac{3(x+2)}{(x+2)(x-3)}+\frac{2 x}{(x-3)(x+4)} \)[/tex]
- [tex]\(\frac{3}{(x-3)}+\frac{2 x}{(x-3)(x+4)}\)[/tex]
- [tex]\(\frac{3(x+4)}{(x-3)(x+4)}+\frac{2 x}{(x-3)(x+4)}\)[/tex]
- [tex]\(\frac{(3(x+4)+2x)}{(x-3)(x+4)}\)[/tex]
These steps lead us to the required result.
