Answer: The work done by the student is not correct.
Explanation:
The given rational expression is,
[tex]\frac{3x+x^2}{3x}[/tex]
Since 3x is the common denominator of 3x and [tex]x^2[/tex].
It can be written as,
[tex]\frac{3x+x^2}{3x}=\frac{3x}{3x}+ \frac{x^2}{3x}[/tex]
Simplify the above expression,
[tex]\frac{3x+x^2}{3x}=1+ \frac{x}{3}[/tex]
So the correct value of the expression is, [tex]1+ \frac{x}{3}[/tex].
According to the student the simplified form of the expression is,
[tex]\frac{3x+x^2}{3x} =1+x^2[/tex]
Which is not correct, because the student takes 3x in denominator of 3x only as shown below,
[tex]\frac{3x+x^2}{3x} =\frac{3x}{3x}+x^2=1+x^2[/tex]
The error made by the student is he didn't take 3x in the denominator of [tex]x^2[/tex].
Therefore, the simplified form written by the student is incorrect.
