I want to continue with this question posted on 7/3/21. Find the difference quotient and simplify your answer. f(x) = x^(2/3) + 1 [f(x) - f(8)]/(x - 8), where x cannot be 8. I will find f(8) first. Note: x^(2/3) = cuberoot{x^2}. cuberoot{x^2} + 1 cuberoot{8^2} + 1 cuberoot{64} + 1 16 + 1 = 17 [cuberoot{x^2} - 17]/( x - 8) Rationalize the numerator. Numerator: [cuberoot{x^2} - 17][cuberoot{x^2} + 17] Denominator: (x - 8)[cuberoot{x^2} + 17] Let cr = cube root [cr{x^2} - 17][cr{x^2} + 17]/(x - 8)[cr{x^2} + 17] Simplify the numerator. Leave denominator alone. Note: (cr{x^2})^2 = x^(4/3) Note: (-17)(17) = -289 Finally, I came up with this: [x^(4/3) - 289]/(x - 8) I don't think this can be simplified further. You say?