Questions: Rearrange this equation to isolate c. a=b(1/c-1/d) c=

Rearrange this equation to isolate c. a=b(1/c-1/d) c=
Transcript text: Rearrange this equation to isolate $c$. \[ a=b\left(\frac{1}{c}-\frac{1}{d}\right) \] \[ c= \]
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Solution

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Solution Steps

Step 1: Start with the given equation

\[ a = b\left(\frac{1}{c} - \frac{1}{d}\right) \]

Step 2: Divide both sides by \( b \) to isolate the term containing \( c \)

\[ \frac{a}{b} = \frac{1}{c} - \frac{1}{d} \]

Step 3: Add \( \frac{1}{d} \) to both sides to isolate \( \frac{1}{c} \)

\[ \frac{a}{b} + \frac{1}{d} = \frac{1}{c} \]

Step 4: Combine the terms on the left side into a single fraction

\[ \frac{ad + b}{bd} = \frac{1}{c} \]

Step 5: Take the reciprocal of both sides to solve for \( c \)

\[ c = \frac{bd}{ad + b} \]

Final Answer

\( c = \frac{bd}{ad + b} \)

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