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.

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

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

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.

Step 1: Set Up the Equation

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

Step 2: Find a Common Denominator

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

Step 3: Equate the Numerators

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

Step 4: Solve for $ x $

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