Questions: 9/(x+1) - 5/2 = 4/(3x+3)

Transcript text: \[ \frac{9}{x+1}-\frac{5}{2}=\frac{4}{3 x+3} \]

Solution

Step 1: Rewrite the Equation

We start with the equation:

\[ \frac{9}{x+1} - \frac{5}{2} = \frac{4}{3x+3} \]

We can rewrite \(3x + 3\) as \(3(x + 1)\).

Step 2: Find a Common Denominator

The least common denominator (LCD) for the fractions is \(6(x + 1)\). We multiply each term by the LCD to eliminate the fractions:

\[ 6(x + 1) \left( \frac{9}{x + 1} - \frac{5}{2} \right) = 6(x + 1) \left( \frac{4}{3(x + 1)} \right) \]

This simplifies to:

\[ 54 - 15(x + 1) = 8 \]

Step 3: Solve the Resulting Equation

Now we simplify and solve the equation:

\[ 54 - 15x - 15 = 8 \]

This leads to:

\[ 39 - 15x = 8 \]

Rearranging gives:

\[ 15x = 31 \quad \Rightarrow \quad x = \frac{31}{15} \approx 2.0667 \]

The solution to the equation is

\[ \boxed{x = 2.0667} \]

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