Final answer:
The solution to the equation (5)/(x+1)-(3)/(2)=(8)/(3x+3) is found by factoring, finding a common denominator, and then simplifying to solve for x, which results in a simplified fraction of x = 5/9.
Step-by-step explanation:
To solve the equation (5)/(x+1)-(3)/(2)=(8)/(3x+3), we need to find a common denominator and combine the terms on each side of the equation. First, we observe that 3x+3 can be factored into 3(x+1).
Now, let's rewrite the equation with this factorization:
(5)/(x+1) - (3)/(2) = (8)/[3(x+1)]
Next, multiply every term by the least common denominator, which is 6(x+1), to eliminate fractions:
5(6) - 3(3)(x+1) = 8(2)
This simplifies to 30 - 9(x+1) = 16, and then to 30 - 9x - 9 = 16.
Upon further simplification, we get -9x + 21 = 16. Subtracting 21 from both sides, we obtain -9x = -5. Dividing by -9 gives the solution for x:
x = 5/9
The solution as a simplified fraction is x = 5/9.