Evaluate the difference quotient and simplify the result

Question

h(x) = x² + x + 2

h(x + Δx) − h(x) / Δx

Δx ≠ 0

Answer 1

The notation has you fouled up!

h(x) = x² + x +2

Let me use the letter k for delta x

h(x+k) = (x+k)² + (x+k) + 2 = x² + 2xk + k² + x + k + 2

h(x+k) - h(x) = 2xk + k + k²

[h(x+k)-h(x)]/k = 2x + 1 + k