Math help? 10 pts best answer!?

Question

ill vote best answer for the person that answers any or all of these questions:

1. how do you simplify 9-(x^(-2))/ (3+(x^(-1)))

2. how do you rewrite (ab-a)/(b^2-b) in the form c(a^n)(b^n)?

3. how do you rewrite a^(-1)/ b^(-1)(sqrt(a))

Answer 1

1) Given expression is 9-(x^(-2))/ (3+(x^(-1)))

                                 = 9 - (1/x^2) / (3 + 1/x)                        [ Since x^-2 = 1/x^2 and x^-1 = 1/x ]

                                 = 9 - (1/x^2) / ((3x + 1)/x)

                                 = 9 - x / x^2(3x + 1)

                                 = 9 - 1/ x(3x + 1)

                                 = 9 - 1 / (3x^2 + x)

                                 = (9(3x^2 + x) -1) / (3x^2 + x)             [ By taking LCM ]

                                 = (27x^2 + 9x - 1) / ((3x^2 + x)

   Therefore 9-(x^(-2))/ (3+(x^(-1)))   = (27x^2 + 9x - 1) / ((3x^2 + x)

Answer 2

2) Given expression is (ab - a) / (b^2 - b)

                                 = a(b - 1) / b(b - 1)

                                 = a / b

                                 = (1) (a^1)(b^-1)   [ This is in the form c(a^n)(b^n) ]

     Therefore (ab - a) / (b^2 - b) = (1) (a^1)(b^-1).

Answer 3

3) Given expression is a^(-1)/ b^(-1)(sqrt(a))

                                 = a^(-1)/ (b^(-1))(√a)     

                                 = (1/a) / (1/b)(√a)                 [ Since a^-1 = 1/a, b^-1 = 1/b ]

                                 = (1/a) / (√a / b)

                                 = b / a√a

    Hence a^(-1)/ b^(-1)(sqrt(a)) can be written as b / a√a.