Questions: Solve for (v). [ frac4v-6-frac6v-6=2 ] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Solve for (v). [ frac4v-6-frac6v-6=2 ] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".
Transcript text: Solve for $v$. \[ \frac{4}{v-6}-\frac{6}{v-6}=2 \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".
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Solution

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Solution Steps

Step 1: Simplify the Equation

The given equation is:

\[ \frac{4}{v-6} - \frac{6}{v-6} = 2 \]

Since the denominators are the same, we can combine the fractions:

\[ \frac{4 - 6}{v-6} = 2 \]

This simplifies to:

\[ \frac{-2}{v-6} = 2 \]

Step 2: Solve for \( v \)

To eliminate the fraction, multiply both sides by \( v-6 \):

\[ -2 = 2(v-6) \]

Distribute the 2 on the right side:

\[ -2 = 2v - 12 \]

Step 3: Isolate \( v \)

Add 12 to both sides to isolate the term with \( v \):

\[ 10 = 2v \]

Divide both sides by 2 to solve for \( v \):

\[ v = 5 \]

Final Answer

The solution to the equation is:

\[ \boxed{v = 5} \]

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