Question

question 28 of 29
rearrange the equation to isolate a.
\\(\left(a + \frac{b}{c}\
ight)(d - e) = f\\)
\\(a = \\)

Explanation:

Step1: Divide both sides by \(d - e\) (assuming \(d - e

eq 0\))
\(\frac{(a + \frac{b}{c})(d - e)}{d - e} = \frac{f}{d - e}\)
Simplifies to: \(a + \frac{b}{c} = \frac{f}{d - e}\)

Step2: Subtract \(\frac{b}{c}\) from both sides

\(a + \frac{b}{c} - \frac{b}{c} = \frac{f}{d - e} - \frac{b}{c}\)
Simplifies to: \(a = \frac{f}{d - e} - \frac{b}{c}\)

(We can also combine the fractions: \(a = \frac{fc - b(d - e)}{c(d - e)}\) or \(a = \frac{fc - bd + be}{c(d - e)}\), but the form from step 2 is also correct as an isolated form for \(a\))

Answer:

\(a = \frac{f}{d - e} - \frac{b}{c}\) (or equivalent combined fraction form)