Mathematics: Astudent does the following to simplify a rational expression. is the work correct? explain any errors and how you would correct them.[tex] rac{3x + x {}^{2} }{3x} = 1 + x {}^{2} [/tex]

6,200 is the answer5 and above give it a shove four and below let it go...

Astudent does the following to simplify a rational

hectol9429

11.03.2022

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.

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