https://file.aiquickdraw.com/mathbot/file/1726808515011ec8qj7b7.jpg

The equation in the image appears to be:

\[
\frac{880}{x} - \frac{858}{x+10} = 1
\]

Let's solve this step-by-step.

1. **Find a common denominator**:
   The denominators are \(x\) and \(x+10\). The common denominator will be \(x(x+10)\).

\[
\frac{880}{x} - \frac{858}{x+10} = 1
\]

Multiply both sides by the common denominator \(x(x+10)\):

\[
880(x+10) - 858x = x(x+10)
\]

2. **Expand both sides**:
   Expand the left and right sides:

\[
880x + 8800 - 858x = x^2 + 10x
\]

3. **Combine like terms**:
   Simplify the left-hand side:

\[
(880x - 858x) + 8800 = x^2 + 10x
\]

\[
22x + 8800 = x^2 + 10x
\]

4. **Move all terms to one side**:
   Subtract \(22x + 8800\) from both sides:

\[
0 = x^2 + 10x - 22x - 8800
\]

\[
0 = x^2 - 12x - 8800
\]

5. **Solve the quadratic equation**:
   Now, solve the quadratic equation \(x^2 - 12x - 8800 = 0\) using the quadratic formula:

\[
x = \frac{-(-12) \pm \sqrt{(-12)^2 - 4(1)(-8800)}}{2(1)}
\]

\[
x = \frac{12 \pm \sqrt{144 + 35200}}{2}
\]

\[
x = \frac{12 \pm \sqrt{35344}}{2}
\]

\[
x = \frac{12 \pm 188}\{2\}
\]

Thus, we get two possible solutions:

\[
x = \frac{12 + 188}{2} = 100
\]
or
\[
x = \frac{12 - 188}{2} = -88
\]

Since \(x\) represents a denominator, we discard the negative value. Therefore, \(x = 100\).

The solution is \(x = 100\).

Would you like further clarification on any step or additional details?

Here are five related questions to expand on this problem:
1. How do you factor quadratic equations without using the quadratic formula?
2. What happens when both solutions to a quadratic equation are negative?
3. How can you check your solution to a rational equation?
4. What are the different methods to solve quadratic equations?
5. Can this problem be solved graphically instead of algebraically?

**Tip**: Always check your final solution by substituting it back into the original equation to ensure accuracy.

Solve the equation: 880/x - 858/(x+10) = 1

This detailed solution explains how to solve the rational equation 880/x - 858/(x+10) = 1 step by step. The solution involves finding a common denominator, expanding, simplifying, and solving a quadratic equation using the quadratic formula. Suitable for students in Grades 9-11.

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