Question: Subtract. v c --- --- v-c c-v v c --- - --- = □ v-c c-v

Subtract.

v c

v-c c-v

v c --- - --- = □ v-c c-v

Solution

Let’s solve the problem step by step.

\[ \frac{v}{v - c} - \frac{c}{c - v} & \]

Since \( c - v = -(v - c) \), we can rewrite the second fraction:

\[ \frac{c}{c - v} = \frac{c}{- (v - c)} = -\frac{c}{v - c} & \]

Now, substitute this back into the original expression:

\[ \frac{v}{v - c} - \frac{c}{c - v} = \frac{v}{v - c} + \frac{c}{v - c} & \]

Combine the numerators over the common denominator:

\[ \frac{v + c}{v - c} & \]

The simplified result is:

\[ \frac{v + c}{v - c} \]