Write this ratio in the simplest form, x sq. - 1/x sq. - x.?

x^2 - 1/x^2 - x

The common denominator will be x^2

x^2 = x^2(x^2/x^2) = x^4/x^2

1/x^2 = 1/x^2

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

x^2 - 1/x^2 - x

= x^4/x^2 - 1/x^2 - x^3/x^2

= (x^4 - 1 - x^3)/x^2

= (x^4 - x^3 - 1)/x^2

Option 2: Do you mean (x^2 - 1)/(x^2 - x)?

Factor each one.

x^2 - 1 is a difference of squares

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

x^2 - x: You can take out a common factor, x.

x^2 - x = x(x-1)

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

= [(x+1)(x-1)]/[x(x-1)]

The (x-1)'s will cancel

Answer: (x+1)/x

x^4-x^3-1 / x^2

x^2 - 1/x^2 - x

=(x^4-x^3-1)/x^2

x2-1/

x2-x

I think the x2's cancel out as 1 and a negative divided by a negative= a positive so it would be 1+1x or in proper mathematical form X+1.

1 over -x2

becuase you simplify x^-1 which ends up being 1 over x

simplify -x and it is -x over one

it is intended to be divided so take the reciprocal of -x over one which becomes 1 over -x

multiply 1 over -x and 1 over - x

so it ends up being 1 over -x^2