Problem of the Week

Updated at Jan 26, 2026 5:29 PM

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

How would you solve \(\frac{v+2}{3}-\frac{5}{4v}=\frac{25}{12}\)?

Check out the solution below!



\[\frac{v+2}{3}-\frac{5}{4v}=\frac{25}{12}\]

1
Multiply both sides by the Least Common Denominator: \(12v\).
\[4v(v+2)-15=25v\]

2
Simplify.
\[4{v}^{2}+8v-15=25v\]

3
Move all terms to one side.
\[4{v}^{2}+8v-15-25v=0\]

4
Simplify  \(4{v}^{2}+8v-15-25v\)  to  \(4{v}^{2}-17v-15\).
\[4{v}^{2}-17v-15=0\]

5
Split the second term in \(4{v}^{2}-17v-15\) into two terms.
\[4{v}^{2}+3v-20v-15=0\]

6
Factor out common terms in the first two terms, then in the last two terms.
\[v(4v+3)-5(4v+3)=0\]

7
Factor out the common term \(4v+3\).
\[(4v+3)(v-5)=0\]

8
Solve for \(v\).
\[v=-\frac{3}{4},5\]

Done

Decimal Form: -0.75, 5
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