Question

Consider the two expressions (6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)/(2x + 3 - 7x - 11) and 4x^2 - 7 + 1/(2x + 3 - 7x - 11)

a) Show that the two expressions represent equal numbers when x = 10

b) Explain why these two expressions do not represent equal numbers when x = -3/2

c) Show that these two expressions represent equal numbers for all x other than -3/2.

Answer 1

Explanation:

a)

(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)(2x + 3 - 7x - 11)

`\sf ((6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8))/((2x + 3 - 7x - 11))`

`\sf = ((6(10)^3 + 9(10)^2 + 4(10) + 7 - 17(10)^2 - 8(10) + 8))/((2(10) + 3 - 7(10) - 11))`

`= ( - 5175)/(58)`

4x^2 - 7 + 1/(2x + 3 - 7x - 11)

`\sf{ 4x^2 - 7 + (1)/((2x + 3 - 7x - 11))}`

`\sf{ 4(10)^2 - 7 + (1)/((2(10) + 3 - 7(10) - 11))}`

`= \sf (22793)/(58)`