Simplify the expression

x^2 + 3x - 28 / x^2 - 7x + 12

Show your work.

(x^4 + - 4 x^3 + 12 x^2 - 28) / x^2

Step-by-step explanation:

Simplify the following:

x^2 + 3 x - 7 x + 12 - 28/x^2

Put each term in x^2 + 3 x - 7 x + 12 - 28/x^2 over the common denominator x^2: x^2 + 3 x - 7 x + 12 - 28/x^2 = x^4/x^2 + (3 x^3) / x^2 - (7 x^3) / x^2 + (12 x^2) / x^2 - 28/x^2:

x^4/x^2 + (3 x^3) / x^2 - (7 x^3) / x^2 + (12 x^2) / x^2 - 28/x^2

x^4/x^2 + (3 x^3) / x^2 - (7 x^3) / x^2 + (12 x^2) / x^2 - 28/x^2 = (x^4 + 3 x^3 - 7 x^3 + 12 x^2 - 28) / x^2:

(x^4 + 3 x^3 - 7 x^3 + 12 x^2 - 28) / x^2

Grouping like terms, x^4 + 3 x^3 - 7 x^3 + 12 x^2 - 28 = x^4 + (3 x^3 - 7 x^3) + 12 x^2 - 28:

(x^4 + (3 x^3 - 7 x^3) + 12 x^2 - 28) / x^2

3 x^3 - 7 x^3 = - 4 x^3:

Answer: (x^4 + - 4 x^3 + 12 x^2 - 28) / x^2