Problem of the Week

Updated at Mar 22, 2021 2:49 PM

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

How would you solve the equation \(\frac{3}{3-{(\frac{5}{m})}^{2}}=\frac{3}{2}\)?

Check out the solution below!



\[\frac{3}{3-{(\frac{5}{m})}^{2}}=\frac{3}{2}\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{3}{3-\frac{{5}^{2}}{{m}^{2}}}=\frac{3}{2}\]

2
Simplify  \({5}^{2}\)  to  \(25\).
\[\frac{3}{3-\frac{25}{{m}^{2}}}=\frac{3}{2}\]

3
Multiply both sides by \(3-\frac{25}{{m}^{2}}\).
\[3=\frac{3}{2}(3-\frac{25}{{m}^{2}})\]

4
Divide both sides by \(3\).
\[1=\frac{1}{2}(3-\frac{25}{{m}^{2}})\]

5
Simplify  \(\frac{3-\frac{25}{{m}^{2}}}{2}\)  to  \(\frac{3}{2}-\frac{\frac{25}{{m}^{2}}}{2}\).
\[1=\frac{3}{2}-\frac{\frac{25}{{m}^{2}}}{2}\]

6
Simplify  \(\frac{\frac{25}{{m}^{2}}}{2}\)  to  \(\frac{25}{2{m}^{2}}\).
\[1=\frac{3}{2}-\frac{25}{2{m}^{2}}\]

7
Subtract \(\frac{3}{2}\) from both sides.
\[1-\frac{3}{2}=-\frac{25}{2{m}^{2}}\]

8
Simplify  \(1-\frac{3}{2}\)  to  \(-\frac{1}{2}\).
\[-\frac{1}{2}=-\frac{25}{2{m}^{2}}\]

9
Multiply both sides by \(2{m}^{2}\).
\[-\frac{1}{2}\times 2{m}^{2}=-25\]

10
Cancel \(2\).
\[-{m}^{2}=-25\]

11
Multiply both sides by \(-1\).
\[{m}^{2}=25\]

12
Take the square root of both sides.
\[m=\pm \sqrt{25}\]

13
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[m=\pm 5\]

Done
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