Question

Select the expression that is equivalent to (2x³+11x²-21x)/x³+3x for x!= -3 or 0, Select the correct choice.

A. 2x+5= 6/x+3
B. 2x+17= 20/x+3
C. 2x+17- 36/x^2+3x
D. 2x+5= 36/x+3

Answer 1

The expression that is equivalent to (2x³+11x²-21x)/x³+3x for x ≠ -3 or 0 is option D.
`\(2x + 5 - (36)/(x+3)\)`

How did we get the value?

To find the expression equivalent to
`\((2x^3+11x^2-21x)/(x^2+3x)\)`, we can use long division. Let us perform the division and compare it with the given options.

2x + 5

_______________

`x^2 + 3x` |
`2x^3 + 11x^2 - 21x`

- (
`2x^3 + 6x^2`)

---------------

`5x^2 - 21x`

-
`(5x^2 + 15x)`

-------------

-36x

-(-36x)

------------

0

So, the result of the division is
`\(2x + 5 - (36)/(x + 3)\)`. Comparing with the options. The correct option is option D.
`\(2x + 5 - (36)/(x+3)\)`

Complete and correct question:

Select the expression that is equivalent to (2x^3+11x^2-21x)/x^2+3x for x ≠-3 or 0. Hint: Use long division.

A) 2x + 5 - 6/x+3

B) 2x + 17 - 20/x+3

C) 2x + 17 - 36/x^2+3x

D) 2x + 5 - 36/x+3