https://file.aiquickdraw.com/mathbot/file/17253697761743qlvucp1.jpg

The uploaded image shows a mathematical equation that appears to involve fractions with variables in the denominators. The equation seems to be:

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

Let's simplify and solve this equation step by step.

### Step 1: Simplify the left-hand side
The first term simplifies immediately since it's \(\frac{x+1}{x+1} = 1\).

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

### Step 2: Combine the left-hand side terms
To combine the left side, rewrite \(1\) as \(\frac{x-1}{x-1}\):

\[
\frac{x-1}{x-1} - \frac{1}{x-1} = \frac{x-2}{x-1}
\]

Simplify:

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

### Step 3: Cross-multiply
To solve the equation, cross-multiply:

\[
(x-2)(x+1) = (x+2)(x-1)
\]

Expand both sides:

\[
x^2 - x - 2 = x^2 - x - 2
\]

The terms on both sides cancel out, suggesting the equation is true for all \(x\) except where the original denominators are zero (\(x \neq 1\)).

### Conclusion
The equation holds true for all values of \(x\) except where the denominators are undefined.

Would you like more details or have any questions?

### Related Questions:
1. How do you solve equations involving rational expressions?
2. What happens if a variable value makes the denominator zero?
3. Can you simplify complex fractions?
4. How does cross-multiplying help in solving rational equations?
5. What are some common mistakes when simplifying rational expressions?

**Tip:** Always check the domain of an equation involving fractions to avoid dividing by zero!

Solve the equation: (x + 1)/(x + 1) - 1/(x - 1) = (x + 2)/(x + 1)

Learn how to solve a rational equation involving cross multiplication and simplification. This problem covers key algebraic concepts, including rational expressions, cross multiplication, and properties of rational expressions. Suitable for high school students in Grades 9-12.

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