Questions: (V-V₁)/(1-c) = V₁/c

Transcript text: \(\left(\frac{V-V_{1}}{1-c}\right)=\frac{V_{1}}{c}\)

Solution

Step 1: Isolate the Variable \( V \)

The given equation is:

\[ \left(\frac{V-V_{1}}{1-c}\right)=\frac{V_{1}}{c} \]

To solve for \( V \), we first multiply both sides by \( 1-c \) to eliminate the fraction on the left side:

\[ V - V_{1} = \frac{V_{1}}{c} \cdot (1-c) \]

Step 2: Simplify the Right Side

Distribute \( \frac{V_{1}}{c} \) on the right side:

\[ V - V_{1} = \frac{V_{1}(1-c)}{c} = \frac{V_{1}}{c} - \frac{V_{1}c}{c} \]

Simplify the expression:

\[ V - V_{1} = \frac{V_{1}}{c} - V_{1} \]

Step 3: Combine Like Terms

Combine the terms on the right side:

\[ V - V_{1} = \frac{V_{1} - V_{1}c}{c} \]

Step 4: Solve for \( V \)

Add \( V_{1} \) to both sides to solve for \( V \):

\[ V = V_{1} + \frac{V_{1} - V_{1}c}{c} \]

Combine the terms:

\[ V = \frac{V_{1}c + V_{1} - V_{1}c}{c} \]

Simplify:

\[ V = \frac{V_{1}}{c} \]

The solution for \( V \) is:

\[ \boxed{V = \frac{V_{1}}{c}} \]

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