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)<…

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.

Step-by-step explanation:

The given rational expression is,

`(3x+x^2)/(3x)`

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

It can be written as,

`(3x+x^2)/(3x)=(3x)/(3x)+ (x^2)/(3x)`

Simplify the above expression,

`(3x+x^2)/(3x)=1+ (x)/(3)`

So the correct value of the expression is,
`1+ (x)/(3)`.

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

`(3x+x^2)/(3x) =1+x^2`

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

`(3x+x^2)/(3x) =(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.