Question

Solve the rational equation, where
x≠2: 4/x-2 +1=7/x-2
Re-order the steps so that the given equation is at the top, the steps are ordered appropriately and the solution is at the bottom.

Answer 1

To solve the rational equation

\[
\frac{4}{x - 2} + 1 = \frac{7}{x - 2}
\]

we can start by isolating the fractions on one side. Here are the steps in order:

1. **Given Equation:**
\[
\frac{4}{x - 2} + 1 = \frac{7}{x - 2}
\]

2. **Subtract \(\frac{4}{x - 2}\) from both sides:**
\[
1 = \frac{7}{x - 2} - \frac{4}{x - 2}
\]

3. **Combine the fractions on the right side:**
\[
1 = \frac{7 - 4}{x - 2}
\]

4. **Simplify the right side:**
\[
1 = \frac{3}{x - 2}
\]

5. **Multiply both sides by \(x - 2\) (where \(x \neq 2\)):**
\[
x - 2 = 3
\]

6. **Add 2 to both sides to solve for \(x\):**
\[
x = 5
\]

7. **Solution:**
\[
x = 5
\]

This is the complete solution to the given rational equation.