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Problem of the Week

Updated at Jan 25, 2021 2:54 PM

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

How can we solve the equation \(\frac{{(3-x)}^{2}}{4(x-3)}=\frac{1}{4}\)?

Check out the solution below!



\[\frac{{(3-x)}^{2}}{4(x-3)}=\frac{1}{4}\]

1
Multiply both sides by \(4(x-3)\).
\[{(3-x)}^{2}=\frac{1}{4}\times 4(x-3)\]

2
Cancel \(4\).
\[{(3-x)}^{2}=x-3\]

3
Expand.
\[9-6x+{x}^{2}=x-3\]

4
Move all terms to one side.
\[9-6x+{x}^{2}-x+3=0\]

5
Simplify  \(9-6x+{x}^{2}-x+3\)  to  \(12-7x+{x}^{2}\).
\[12-7x+{x}^{2}=0\]

6
Factor \(12-7x+{x}^{2}\).
\[(x-4)(x-3)=0\]

7
Solve for \(x\).
\[x=4,3\]

8
Check solution
When \(x=3\), the original equation \(\frac{{(3-x)}^{2}}{4(x-3)}=\frac{1}{4}\) does not hold true.
We will drop \(x=3\) from the solution set.

9
Therefore,
\(x=4\)

Done
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