Question

Arrange the expressions in ascending order of their values when x = -2.

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

Answer 1

Explanation:

Option (1)

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

Put x = -2, let the value is y such that,

`y=(1-(-2)^2)/(1-2(-2))\\\\=(1-4)/(1+4)\\\\=-0.6`

Option (2)

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

Put x = -2, let the value is y such that,

`y=((-2)^2-1)/(1-2(-2))\\\\=(4-1)/(1+4)\\\\=0.6`

Option 3)

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

Put x=-2 such that,

`y=2(-2)^2+((-2))/(2)\\\\=7`

Option (4)

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

Put x =-2 such that,

`y=3(-2)^2+(1)/(2((-2)-1))\\\\=11.83`

Ascending values : -0.6,0.6,7,11.83

or

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