Question

solve for u.
\\(\frac{5}{3u} - \frac{7}{u} = 1\\)
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
\\(u = \square\\)

Explanation:

Step1: Find common denominator

The common denominator of \(3u\) and \(u\) is \(3u\). Rewrite \(\frac{7}{u}\) as \(\frac{21}{3u}\).
The equation becomes \(\frac{5}{3u}-\frac{21}{3u}=1\).

Step2: Combine fractions

Subtract the numerators: \(\frac{5 - 21}{3u}=1\), which simplifies to \(\frac{-16}{3u}=1\).

Step3: Solve for \(u\)

Multiply both sides by \(3u\): \(-16 = 3u\).
Then divide both sides by \(3\): \(u=-\frac{16}{3}\).

Step4: Check for validity

Since \(u = -\frac{16}{3}\) does not make the original denominators \(3u\) or \(u\) equal to zero, it is a valid solution.

Answer:

\(u = -\frac{16}{3}\)