Solve this question? 2x3+x2+2x+1 / x3-x2+x-1Question in test could not answer

Supposing that you need to reduce the fraction to its
lowest terms, you need to factorize both numerator and
denominator.

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

You need to factorize the numerator, hence you need to
group the terms such that:

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

You need to factor out 2x + 1 such
that:

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

You need to factorize the denominator, hence you need
to group the terms such that:

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

You need to factor out x - 1 such
that:

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

You need to write the factored form of fraction such
that:

`((2x + 1)(x^2 + 1))/((x - 1)(x^2 +
1))`

Notice that the factored form accentuates the common
factors, hence you need to reduce these factors such
that:

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

Hence, simplifying the fraction to its
lowest terms yields `(2x^3 + x^2 + 2x + 1)/(x^3 - x^2 + x - 1) = (2x + 1)/(x - 1).`