Final answer:
To subtract fractions, we need to find a common denominator. Then, we simplify the expression by expanding and combining like terms, and finally, we simplify as much as possible.
Step-by-step explanation:
To subtract (x+1)/(x+3) - (2x-4)/(5x+15), we need to find a common denominator. The common denominator is (x+3)(5x+15).
Now, we can rewrite the equation using the common denominator:
((x+1)(5x+15) - (2x-4)(x+3))/(common denominator)
Next, we simplify by expanding and combining like terms:
(5x^2 + 20x + 15 - 2x^2 + 4x + 12)/(common denominator)
(3x^2 + 24x + 27)/(common denominator)
Finally, we simplify the expression as much as possible. There are no common factors in the numerator and denominator that can be cancelled out, so the result is:
3x^2 + 24x + 27)/(x^2 + 8x + 9)