11/x-9=11/9

To solve the equation \( \frac{11}{x} - 9 = \frac{11}{9} \), follow these steps:

1. Isolate the term with \( x \): Start by adding 9 to both sides of the equation: \[ \frac{11}{x} = \frac{11}{9} + 9 \]

2. Convert 9 to a fraction: To add the fractions, convert 9 to a fraction with a denominator of 9. This can be written as: \[ 9 = \frac{81}{9} \] Now the equation becomes: \[ \frac{11}{x} = \frac{11}{9} + \frac{81}{9} \] Combine the fractions on the right side: \[ \frac{11}{x} = \frac{11 + 81}{9} = \frac{92}{9} \]

3. Cross-multiply: Now, you can cross-multiply to eliminate the fractions: \[ 11 \cdot 9 = 92 \cdot x \] This simplifies to: \[ 99 = 92x \]

4. Solve for \( x \): Now, divide both sides by 92: \[ x = \frac{99}{92} \]

Thus, the solution is: \[ x = \frac{99}{92} \]