4/n=1/a+1/b+1/c Solve the equation
To solve the equation
\[
\frac{4}{n} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c},
\]
let's first get a common denominator for the right-hand side. The common denominator for \( a \), \( b \), and \( c \) is \( abc \). Thus, we can rewrite the right-hand side:
\[
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{bc}{abc} + \frac{ac}{abc} + \frac{ab}{abc} = \frac{bc + ac + ab}{abc}.
\]
Now we can rewrite the original equation as:
\[
\frac{4}{n} = \frac{bc + ac + ab}{abc}.
\]
Next, cross-multiply to eliminate the fractions:
\[
4 \cdot abc = n(bc + ac + ab).
\]
This gives us the equation:
\[
n(bc + ac + ab) = 4abc.
\]
Now, we can solve for \( n \):
\[
n = \frac{4abc}{bc + ac + ab}.
\]
This expression provides a relationship for \( n \) in terms of \( a \), \( b \), and \( c \). The solution \( n \) depends on the values of \( a \), \( b \), and \( c \).