Question

A student does the following to simplify a rational expression. Is the work correct? Explain any errors and how you would correct them.
$\frac{3x + x {}^{2} }{3x} = 1 + x {}^{2}$

Answer 1

Answer: The work done by the student is not correct.

Explanation:

The given rational expression is,

$\frac{3x+x^2}{3x}$

Since 3x is the common denominator of 3x and $x^2$.

It can be  written as,

$\frac{3x+x^2}{3x}=\frac{3x}{3x}+ \frac{x^2}{3x}$

Simplify the above expression,

$\frac{3x+x^2}{3x}=1+ \frac{x}{3}$

So the correct value of the expression is, $1+ \frac{x}{3}$.

According to the student the simplified form of the expression is,

$\frac{3x+x^2}{3x} =1+x^2$

Which is not correct, because the student takes 3x in denominator of 3x only as shown below,

$\frac{3x+x^2}{3x} =\frac{3x}{3x}+x^2=1+x^2$

The error made by the student is he didn't take 3x in the denominator of $x^2$.

Therefore, the simplified form written by the student is incorrect.