Question

solve for u.
\\(\frac{3}{u - 6}= -\frac{4}{3u - 18}+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: Simplify the denominator

Notice that \(3u - 18 = 3(u - 6)\). So the equation becomes \(\frac{3}{u - 6}=-\frac{4}{3(u - 6)}+1\).

Step2: Multiply both sides by \(3(u - 6)\) (note \(u

eq6\))
\(3\times3=- 4+3(u - 6)\).

Step3: Simplify left and right sides

Left side: \(9\). Right side: \(-4 + 3u-18=3u-22\). So we have \(9 = 3u-22\).

Step4: Solve for \(u\)

Add 22 to both sides: \(9 + 22=3u\), so \(31 = 3u\), then \(u=\frac{31}{3}\).

Step5: Check the solution

Substitute \(u = \frac{31}{3}\) into the original equation. The denominators \(u - 6=\frac{31}{3}-6=\frac{31 - 18}{3}=\frac{13}{3}
eq0\) and \(3u - 18=3\times\frac{31}{3}-18 = 31 - 18 = 13
eq0\). So the solution is valid.

Answer:

\(\frac{31}{3}\)