Problem of the Week

Updated at Jul 20, 2026 4:59 PM

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

How would you solve \(3-\frac{5}{2+\frac{5}{p}}=\frac{19}{13}\)?

Check out the solution below!



\[3-\frac{5}{2+\frac{5}{p}}=\frac{19}{13}\]

1
Subtract \(3\) from both sides.
\[-\frac{5}{2+\frac{5}{p}}=\frac{19}{13}-3\]

2
Simplify  \(\frac{19}{13}-3\)  to  \(-\frac{20}{13}\).
\[-\frac{5}{2+\frac{5}{p}}=-\frac{20}{13}\]

3
Multiply both sides by \(2+\frac{5}{p}\).
\[-5=-\frac{20}{13}(2+\frac{5}{p})\]

4
Move the negative sign to the left.
\[-5=-\frac{20(2+\frac{5}{p})}{13}\]

5
Multiply both sides by \(13\).
\[-5\times 13=-20(2+\frac{5}{p})\]

6
Simplify  \(-5\times 13\)  to  \(-65\).
\[-65=-20(2+\frac{5}{p})\]

7
Divide both sides by \(-20\).
\[\frac{-65}{-20}=2+\frac{5}{p}\]

8
Two negatives make a positive.
\[\frac{65}{20}=2+\frac{5}{p}\]

9
Simplify  \(\frac{65}{20}\)  to  \(\frac{13}{4}\).
\[\frac{13}{4}=2+\frac{5}{p}\]

10
Subtract \(2\) from both sides.
\[\frac{13}{4}-2=\frac{5}{p}\]

11
Simplify  \(\frac{13}{4}-2\)  to  \(\frac{5}{4}\).
\[\frac{5}{4}=\frac{5}{p}\]

12
Multiply both sides by \(p\).
\[\frac{5}{4}p=5\]

13
Simplify  \(\frac{5}{4}p\)  to  \(\frac{5p}{4}\).
\[\frac{5p}{4}=5\]

14
Multiply both sides by \(4\).
\[5p=5\times 4\]

15
Simplify  \(5\times 4\)  to  \(20\).
\[5p=20\]

16
Divide both sides by \(5\).
\[p=\frac{20}{5}\]

17
Simplify  \(\frac{20}{5}\)  to  \(4\).
\[p=4\]

Done
Cymath foriOSAndroid