What is the solution(s) of the equation 2x−3xx+3=xx+3

Question

2
𝑥
−
3
𝑥
𝑥
+
3
=
𝑥
𝑥
+
3
?(1 point)
Responses

32
3
2
Start Fraction 3 over 2 End Fraction

−1
−
1
negative 1

1 and −32
−
3
2
1 and negative Start Fraction 3 over 2 End Fraction

−1
−
1
and 32

Answer 1

To solve the equation \( \frac{2x - 3}{x + 3} = \frac{x}{x + 3} \), we can cross-multiply, as the denominators are the same (assuming \( x \neq -3 \) to avoid division by zero):

\[ 2x - 3 = x \]

Now, subtract \( x \) from both sides:

\[ 2x - x - 3 = 0 \]

This simplifies to:

\[ x - 3 = 0 \]

Adding \( 3 \) to both sides gives:

\[ x = 3 \]

We must verify that the solution does not make the denominator zero. For this equation, the denominator \( x + 3 \) equals \( 6 \) when \( x = 3 \), which is non-zero.

Thus, the only solution is:

\[ \boxed{3} \]