https://file.aiquickdraw.com/mathbot/file/1725977131012vdx721f6.jpg

The image appears to contain an algebraic expression, though it is upside down. From what I can see, the expression reads:

\[
9 \div x - \frac{7}{x} = 6
\]

Let's solve this step by step:

### Step 1: Write the equation in standard form:
\[
\frac{9}{x} - \frac{7}{x} = 6
\]

### Step 2: Simplify the left side:
Both terms on the left side have the same denominator, so we can combine them:
\[
\frac{9 - 7}{x} = 6
\]

This simplifies to:
\[
\frac{2}{x} = 6
\]

### Step 3: Solve for \( x \):
Now, solve for \( x \) by multiplying both sides of the equation by \( x \) to get rid of the denominator:
\[
2 = 6x
\]

Then, divide both sides by 6 to isolate \( x \):
\[
x = \frac{2}{6} = \frac{1}{3}
\]

Thus, the solution is:
\[
x = \frac{1}{3}
\]

Would you like more details or have any questions?

Here are some related questions to expand on this topic:
1. What happens if there is an additional term on the left-hand side of the equation?
2. How can we apply the same method if the denominators are different?
3. Can we solve similar equations with different values on the right-hand side?
4. What if the equation involved \( x^2 \) instead of \( x \)?
5. How would you graph this equation to understand its solution better?

**Tip:** When solving equations with fractions, always look for opportunities to combine terms with the same denominator for easier simplification.

What is the solution to the equation 9 ÷ x - 7/x = 6?

Learn how to solve the rational equation 9 ÷ x - 7/x = 6 step by step. This algebra problem involves combining terms with common denominators and solving for x. Suitable for students in Grades 7-9.

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