rearrange\:the\:eqation\:to\:solve\:for\:f\:\left(a-\frac{b}{c}\right)\left(\frac{d}{e}+f\right)=g

To rearrange the equation to solve for \( f \):

\[
\left(a - \frac{b}{c}\right)\left(\frac{d}{e} + f\right) = g
\]

### Step 1: Expand the Left Side
First, distribute the term \( \left(a - \frac{b}{c}\right) \) over the sum inside the parentheses:

\[
\left(a - \frac{b}{c}\right) \cdot \frac{d}{e} + \left(a - \frac{b}{c}\right) \cdot f = g
\]

### Step 2: Simplify the Expression
This simplifies to:

\[
\frac{ad}{e} - \frac{bd}{ce} + \left(a - \frac{b}{c}\right)f = g
\]

### Step 3: Isolate the Term Involving \( f \)
Subtract the non-\( f \) term from both sides:

\[
\left(a - \frac{b}{c}\right)f = g - \frac{ad}{e} + \frac{bd}{ce}
\]

### Step 4: Solve for \( f \)
Finally, divide both sides by \( \left(a - \frac{b}{c}\right) \):

\[
f = \frac{g - \frac{ad}{e} + \frac{bd}{ce}}{a - \frac{b}{c}}
\]

This rearranged equation solves for \( f \).

Do you need further explanation or have any questions?

Here are 5 related questions to consider:

1. What happens to the equation if \( a = \frac{b}{c} \)?
2. How would the solution change if \( g = 0 \)?
3. Can you factor \( \frac{ad}{e} - \frac{bd}{ce} \) for simplification?
4. How would you solve the equation for \( a \) instead of \( f \)?
5. What if \( f = 0 \)? What does the equation simplify to?

**Tip:** When isolating a variable, always check if there are common factors you can simplify to make the equation easier to solve.

Learn how to rearrange the equation (a - b/c)(d/e + f) = g to solve for f with a detailed step-by-step solution. This problem involves algebraic manipulation using the distributive property and is suitable for high school students.

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