https://file.aiquickdraw.com/mathbot/file/17273633542035cqnwr2z.jpg

The equation in the image appears to be a complex algebraic expression involving fractions. Here's how it can be interpreted:

\[
\frac{1}{\frac{1}{x - a}} + \frac{1}{\frac{1}{x - b}} = a + b
\]

This equation includes two terms on the left-hand side, both involving fractions within fractions, and the result is given as \(a + b\).

Let me simplify this step-by-step:

### Step 1: Simplify each term on the left-hand side
Each term on the left-hand side is a fraction with another fraction in the denominator. To simplify these, use the property:

\[
\frac{1}{\frac{1}{x - a}} = x - a
\]

Similarly:

\[
\frac{1}{\frac{1}{x - b}} = x - b
\]

Thus, the equation becomes:

\[
(x - a) + (x - b) = a + b
\]

### Step 2: Simplify the equation
Now, combine the terms on the left-hand side:

\[
x - a + x - b = a + b
\]

Simplify the terms further:

\[
2x - (a + b) = a + b
\]

### Step 3: Solve for \(x\)
Now, add \((a + b)\) to both sides of the equation:

\[
2x = 2(a + b)
\]

Finally, divide both sides by 2 to isolate \(x\):

\[
x = a + b
\]

### Final Result:
The solution to the equation is:

\[
x = a + b
\]

Would you like further clarification on any step, or do you have any questions about this? 

Here are five related questions for further exploration:

1. How do you simplify nested fractions in algebra?
2. What are the common strategies to solve linear equations?
3. Can this type of equation be extended to more variables or terms?
4. How does cross-multiplying help in solving algebraic fractions?
5. What are some applications of such algebraic equations in real-world problems?

**Tip:** Always simplify inner fractions before working on the overall equation. This reduces the complexity and makes solving the equation easier.

Solve the equation: \frac{1}{\frac{1}{x - a}} + \frac{1}{\frac{1}{x - b}} = a + b

Learn how to solve an algebraic equation involving nested fractions, simplified step-by-step. This problem focuses on key algebraic concepts such as fraction simplification and solving linear equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation