Consider the two expressions $\frac{6x^3+19x^2-4x+5}{2x+1}$ and $5x^2-8+\frac1{2x+1}.$
a) Show that the two expressions represent equal numbers when $x=10.$
b) Explain why these two expressions do not represent equal numbers when $x=\dfrac12.$
c) Show that these two expressions represent equal numbers for all $x$ other than $\dfrac12.$