To solve the equation
[tex]\[
-2 = \frac{x}{x+3} - \frac{-3}{x+3}
\][/tex]
let's follow these steps:
1. First, simplify the right-hand side of the equation [tex]\(\frac{x}{x+3} - \frac{-3}{x+3}\)[/tex]:
[tex]\[
\frac{x}{x+3} - \frac{-3}{x+3} = \frac{x + 3}{x+3}
\][/tex]
2. Notice that [tex]\(\frac{x + 3}{x+3} = 1\)[/tex] for [tex]\(x \neq -3\)[/tex].
3. Now, the equation becomes:
[tex]\[
-2 = 1
\][/tex]
4. This statement ([tex]\(-2 = 1\)[/tex]) is a contradiction. Therefore, the original equation does not hold for any value of [tex]\(x\)[/tex].
5. Since there is no value of [tex]\(x\)[/tex] that satisfies the equation:
We conclude that there is no solution.
Solution:
[tex]\[ \boxed{\text{No solution}} \][/tex]
