Questions: Solve the equation. 5/(9x+9) = 5/(x+1) - 4/9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are x= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.

Solution Steps

To solve the given equation, we need to find the value of $x$ that satisfies the equation. We will start by eliminating the fractions by finding a common denominator and then solve the resulting linear equation.

We start with the given equation: $$\frac{5}{9x + 9} = \frac{5}{x + 1} - \frac{4}{9}$$

To eliminate the fractions, we find a common denominator for the terms on the right-hand side: $$\frac{5}{x + 1} - \frac{4}{9} = \frac{5 \cdot 9 - 4 \cdot (x + 1)}{9(x + 1)} = \frac{45 - 4x - 4}{9(x + 1)} = \frac{41 - 4x}{9(x + 1)}$$

Since the denominators are now the same, we can equate the numerators: $$5 = 41 - 4x$$

Rearrange the equation to solve for $x$: $$5 = 41 - 4x \implies 4x = 41 - 5 \implies 4x = 36 \implies x = \frac{36}{4} = 9$$

Final Answer