$$ \frac{3}{x+2}-\frac{5}{x-6}=\frac{3 x-1}{x^{2}-4 x-12} $$ Identify the Step in which the very FIRST error occurs, or indicate that there is not an error in the problem. Step 1: $$ \frac{3(x-6)}{(x+2)(x-6)}-\frac{5(x+2)}{(x-6)(x+2)}=\frac{3 x-1}{(x+2)(x-6)} $$ Step 2: $$ \frac{3 x-18}{(x+2)(x-6)}-\frac{5 x+10}{(x+2)(x-6)}=\frac{3 x-1}{(x+2)(x-6)} $$ Step 3: $$ \frac{3 x-18-5 x+10}{(x+2)(x-6)}=\frac{3 x-1}{(x+2)(x-6)} $$ Step 4: $$ \frac{-2 x-8}{(x+2)(x-6)}=\frac{3 x-1}{(x+2)(x-6)} $$ Step 5: $$ -2 x-8=3 x-1 $$ Step 6: $$ -5 x=7 $$ Step 7: $$ x=-\frac{7}{5} $$

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UpStudy AI · Accepted Answer

Let's analyze the steps provided to identify if there is an error and, if so, where it occurs.

### Step 1:
The equation is transformed correctly by finding a common denominator:
$$
\frac{3(x-6)}{(x+2)(x-6)} - \frac{5(x+2)}{(x-6)(x+2)} = \frac{3x-1}{(x+2)(x-6)}
$$
This step is correct.

### Step 2:
The numerators are expanded:
$$
\frac{3x - 18}{(x+2)(x-6)} - \frac{5x + 10}{(x+2)(x-6)} = \frac{3x - 1}{(x+2)(x-6)}
$$
This step is also correct.

### Step 3:
The numerators are combined:
$$
\frac{3x - 18 - 5x - 10}{(x+2)(x-6)} = \frac{3x - 1}{(x+2)(x-6)}
$$
Here, the left side simplifies to:
$$
3x - 18 - 5x - 10 = -2x - 28
$$
So, it should be:
$$
\frac{-2x - 28}{(x+2)(x-6)} = \frac{3x - 1}{(x+2)(x-6)}
$$
This indicates an error in the simplification of the left side.

### Step 4:
The equation is incorrectly stated as:
$$
\frac{-2x - 8}{(x+2)(x-6)} = \frac{3x - 1}{(x+2)(x-6)}
$$
This is where the first error occurs. The left side should have been $$-2x - 28$$ instead of $$-2x - 8$$.

### Conclusion:
The very first error occurs in **Step 3**, where the simplification of the left side was incorrect. The correct expression should have been $$-2x - 28$$ instead of $$-2x - 8$$.
The first error occurs in Step 3.

Identify the Step in which the very FIRST error occurs, or indicate that there is not an error in the problem.
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:

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