Final answer:
To simplify the addition of (-4)/(x+2) + (9)/(x-3), first find a common denominator, which is (x+2)(x-3). Rewrite each fraction with the common denominator and combine like terms. The final simplified form is (5x + 30)/((x+2)(x-3)).
Step-by-step explanation:
To add or subtract fractions, we need a common denominator. In the case of the ratio (-4)/(x+2) + (9)/(x-3), the denominators are (x+2) and (x-3). We need to find a common denominator which is the product of these two, giving us (x+2)(x-3).
Next, we rewrite each fraction with the common denominator:
- The first fraction becomes (-4)(x-3)/((x+2)(x-3))
- The second fraction becomes (9)(x+2)/((x+2)(x-3))
Now, we combine the numerators over the common denominator:
(-4x + 12 + 9x + 18)/((x+2)(x-3))
Combining like terms in the numerator:
(5x + 30)/((x+2)(x-3))
Finally, there are no further simplifications that can be made unless we have more information about the variable x, so this is the simplified form of the given ratio.