Solve the fractional equation $\frac{2x + 2}{x - 2} = 5$. We need to check the solution in the original equation and, if there is no solution, enter NO SOLUTION.

1. Problem Description

Solve the fractional equation $\frac{2x + 2}{x - 2} = 5$. We need to check the solution in the original equation and, if there is no solution, enter NO SOLUTION.

2. Solution Steps

The equation is $\frac{2x + 2}{x - 2} = 5$.

First, multiply both sides of the equation by $(x-2)$ to eliminate the fraction:

$2x + 2 = 5(x - 2)$

$2x + 2 = 5x - 10$

Next, we subtract $2x$ from both sides:

$2 = 3x - 10$

Then, add 10 to both sides:

$12 = 3x$

Finally, divide both sides by 3:

$x = \frac{12}{3} = 4$

Now we check the solution $x = 4$ in the original equation:

$\frac{2(4) + 2}{4 - 2} = \frac{8 + 2}{2} = \frac{10}{2} = 5$

Since this is true, the solution is $x=4$.

3. Final Answer

4