To solve the equation \( \frac{9}{x+1} - \frac{5}{2} = \frac{6}{3x+3} \), we can follow these steps:

### Step 1: Simplify the equation
Notice that \( 3x + 3 \) can be factored as \( 3(x + 1) \), so we rewrite the equation as:

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

We can simplify \( \frac{6}{3(x+1)} \) to \( \frac{2}{x+1} \):

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

### Step 2: Combine like terms
Now, subtract \( \frac{2}{x+1} \) from \( \frac{9}{x+1} \):

\[
\frac{9 - 2}{x+1} - \frac{5}{2} = 0
\]

This simplifies to:

\[
\frac{7}{x+1} = \frac{5}{2}
\]

### Step 3: Cross-multiply to solve for \( x \)
Cross-multiply to eliminate the fractions:

\[
7 \times 2 = 5 \times (x + 1)
\]

Simplify:

\[
14 = 5x + 5
\]

### Step 4: Isolate \( x \)
Subtract 5 from both sides:

\[
9 = 5x
\]

Now, divide by 5:

\[
x = \frac{9}{5}
\]

### Final Answer:
The solution is \( x = \frac{9}{5} \) or \( x = 1.8 \).

Would you like further details or explanations? Here are some related questions:

1. How do we solve similar equations with different fractions?
2. What if the equation had a quadratic term instead?
3. How can we verify our solution?
4. What happens if we have more complicated denominators?
5. How does cross-multiplication work with inequalities?

**Tip:** Always look for common factors or opportunities to simplify fractions before solving the equation.

Learn how to solve the equation 9/(x+1) - 5/2 = 6/(3x+3) with a detailed step-by-step solution. This problem involves equations with fractions and requires knowledge of cross-multiplication and algebraic manipulation. Suitable for Grades 9-12 students and those preparing for advanced algebra concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation