Problem of the Week

Updated at Jul 14, 2025 11:49 AM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation \(6-{(\frac{3}{3-u})}^{2}=\frac{15}{4}\)?

Check out the solution below!



\[6-{(\frac{3}{3-u})}^{2}=\frac{15}{4}\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[6-\frac{{3}^{2}}{{(3-u)}^{2}}=\frac{15}{4}\]

2
Simplify  \({3}^{2}\)  to  \(9\).
\[6-\frac{9}{{(3-u)}^{2}}=\frac{15}{4}\]

3
Subtract \(6\) from both sides.
\[-\frac{9}{{(3-u)}^{2}}=\frac{15}{4}-6\]

4
Simplify  \(\frac{15}{4}-6\)  to  \(-\frac{9}{4}\).
\[-\frac{9}{{(3-u)}^{2}}=-\frac{9}{4}\]

5
Multiply both sides by \({(3-u)}^{2}\).
\[-9=-\frac{9}{4}{(3-u)}^{2}\]

6
Simplify  \(\frac{9}{4}{(3-u)}^{2}\)  to  \(\frac{9{(3-u)}^{2}}{4}\).
\[-9=-\frac{9{(3-u)}^{2}}{4}\]

7
Multiply both sides by \(4\).
\[-9\times 4=-9{(3-u)}^{2}\]

8
Simplify  \(-9\times 4\)  to  \(-36\).
\[-36=-9{(3-u)}^{2}\]

9
Divide both sides by \(-9\).
\[\frac{-36}{-9}={(3-u)}^{2}\]

10
Two negatives make a positive.
\[\frac{36}{9}={(3-u)}^{2}\]

11
Simplify  \(\frac{36}{9}\)  to  \(4\).
\[4={(3-u)}^{2}\]

12
Take the square root of both sides.
\[\pm \sqrt{4}=3-u\]

13
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[\pm 2=3-u\]

14
Switch sides.
\[3-u=\pm 2\]

15
Break down the problem into these 2 equations.
\[3-u=2\]
\[3-u=-2\]

16
Solve the 1st equation: \(3-u=2\).
\[u=1\]

17
Solve the 2nd equation: \(3-u=-2\).
\[u=5\]

18
Collect all solutions.
\[u=1,5\]

Done
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