Mathematics, 15.07.2019 07:30 serenityarts123

Will give brainliest simplify (1/x^2+2x+/x^2+x-2) can you show me the steps in detail because i am very confused

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Simplify the following:
2 x + 1 + 1/x^2 - (1/x^2 + x - 2)

Put each term in x - 2 + 1/x^2 over the common denominator x^2: x - 2 + 1/x^2 = x^3/x^2 - (2 x^2)/x^2 + 1/x^2:
2 x + 1 + 1/x^2 - x^3/x^2 - (2 x^2)/x^2 + 1/x^2

x^3/x^2 - (2 x^2)/x^2 + 1/x^2 = (x^3 - 2 x^2 + 1)/x^2:
1/x^2 + 2 x + 1 - (x^3 - 2 x^2 + 1)/x^2

The possible rational roots of x^3 - 2 x^2 + 1 are x = ± 1. Of these, x = 1 is a root. This gives x - 1 as all linear factors:
1/x^2 + 2 x + 1 - (((x - 1) (x^3 - 2 x^2 + 1))/(x - 1))/(x^2)

| |
x | - | 1 | | x^2 | - | x | - | 1
x^3 | - | 2 x^2 | + | 0 | + | 1
x^3 | - | x^2 | | | |
| | -x^2 | + | 0 | |
| | -x^2 | + | x | |
| | | | -x | + | 1
| | | | -x | + | 1
| | | | | | 0:
1/x^2 + 2 x + 1 - (x^2 - x - 1 (x - 1))/x^2

Put each term in x^(-2) + 2 x + 1 - ((x - 1) (x^2 - x - 1))/x^2 over the common denominator x^2: x^(-2) + 2 x + 1 - ((x - 1) (x^2 - x - 1))/x^2 = 1/x^2 + (2 x^3)/x^2 + x^2/x^2 - ((x - 1) (x^2 - x - 1))/x^2:1/x^2 + (2 x^3)/x^2 + x^2/x^2 - ((x - 1) (x^2 - x - 1))/x^2
1/x^2 + (2 x^3)/x^2 + x^2/x^2 - ((x - 1) (x^2 - x - 1))/x^2 = (1 + 2 x^3 + x^2 - (x - 1) (x^2 - x - 1))/x^2:(1 + 2 x^3 + x^2 - (x - 1) (x^2 - x - 1))/x^2

| | | | x | - | 1
| | x^2 | - | x | - | 1
| | | | -x | + | 1
| | -x^2 | + | x | + | 0
x^3 | - | x^2 | + | 0 | + | 0
x^3 | - | 2 x^2 | + | 0 | + | 1:
(-x^3 - 2 x^2 + 1 + 2 x^3 + x^2 + 1)/x^2

-(x^3 - 2 x^2 + 1) = -x^3 + 2 x^2 - 1:
(-x^3 + 2 x^2 - 1 + 2 x^3 + x^2 + 1)/x^2

Grouping like terms, 2 x^3 - x^3 + 2 x^2 + x^2 - 1 + 1 = (2 x^3 - x^3) + (x^2 + 2 x^2) + (1 - 1):
((2 x^3 - x^3) + (x^2 + 2 x^2) + (1 - 1))/x^2

2 x^3 - x^3 = x^3:
(x^3 + (x^2 + 2 x^2) + (1 - 1))/x^2

x^2 + 2 x^2 = 3 x^2:
(x^3 + 3 x^2 + (1 - 1))/x^2

1 - 1 = 0:
(x^3 + 3 x^2)/x^2

Factor x^2 out of x^3 + 3 x^2:
(x^2 (x + 3))/x^2

(x^2 (x + 3))/x^2 = x^2/x^2×(x + 3) = x + 3:
x + 3

Answer from: Quest

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a) |-1|, |3/2|, |-2|, |-3|, |3.5|

Answer from: Quest

Ineed show the photo because i need more information

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