Question

solve for u.
\\(\frac{7}{u^2 - 8u + 15} = \frac{1}{u - 3} + \frac{2}{u - 5}\\)
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
u = \\(\square\\)

Explanation:

Step1: Factor the denominator

Factor \(u^2 - 8u + 15\) as \((u - 3)(u - 5)\). So the equation becomes \(\frac{7}{(u - 3)(u - 5)}=\frac{1}{u - 3}+\frac{2}{u - 5}\).

Step2: Multiply both sides by \((u - 3)(u - 5)\)

Multiply each term by \((u - 3)(u - 5)\) to eliminate denominators: \(7 = (u - 5)+2(u - 3)\).

Step3: Simplify the right - hand side

Expand the right - hand side: \(7=u - 5 + 2u-6\). Combine like terms: \(7 = 3u-11\).

Step4: Solve for u

Add 11 to both sides: \(7 + 11=3u\), so \(18 = 3u\). Divide both sides by 3: \(u = 6\).

Step5: Check for extraneous solutions

We need to check if \(u = 6\) makes the original denominators zero. For \(u-3=6 - 3=3
eq0\) and \(u - 5=6 - 5 = 1
eq0\), so \(u = 6\) is a valid solution.

Answer:

\(u = 6\)