Final answer:
To add (3x+5)/(x²+3x-18) and (3)/(x²+5x-6), find the least common denominator (LCD), adjust each fraction to have the LCD, add the numerators, and simplify the result.
Step-by-step explanation:
The question requires us to add the expressions (3x+5)/(x²+3x-18) and (3)/(x²+5x-6) by finding a common denominator and combining the terms. Since adding fractions requires a common denominator, we will first factor both denominators to determine the least common denominator. The denominators factor into (x+6)(x-3) and (x+6)(x-1) respectively. The least common denominator (LCD) would be the product of unique factors, thus, it is (x+6)(x-3)(x-1).
To add these fractions, we multiply the numerator and denominator of each fraction by any factors that are missing from its denominator to match the LCD. Then, we add the resulting numerators while keeping the denominator the same. After simplifying if necessary, we'll have the sum of the two given expressions.