## Solving the Equation: (x+2)^2 / (2x-3) - 1 = (x^2+10) / (2x-3)

This article will guide you through the steps of solving the equation:

**(x+2)^2 / (2x-3) - 1 = (x^2+10) / (2x-3)**

### 1. Simplifying the Equation

To begin, we need to simplify the equation. Let's combine the terms on the left side:

**(x+2)^2 / (2x-3) - (2x-3) / (2x-3) = (x^2+10) / (2x-3)**

Now, we can combine the numerators on the left side:

**[(x+2)^2 - (2x-3)] / (2x-3) = (x^2+10) / (2x-3)**

### 2. Expanding and Combining Terms

Next, we expand the square on the left side:

**(x^2 + 4x + 4 - 2x + 3) / (2x-3) = (x^2+10) / (2x-3)**

Combining like terms, we get:

**(x^2 + 2x + 7) / (2x-3) = (x^2+10) / (2x-3)**

### 3. Eliminating the Denominators

Since both sides of the equation have the same denominator, we can multiply both sides by (2x-3) to eliminate the denominators:

**(x^2 + 2x + 7) = (x^2 + 10)**

### 4. Solving for x

Now, we can solve for *x* by simplifying the equation further:

**2x + 7 = 10**

**2x = 3**

**x = 3/2**

### Conclusion

Therefore, the solution to the equation **(x+2)^2 / (2x-3) - 1 = (x^2+10) / (2x-3)** is **x = 3/2**.