Consider the two expressions $\frac{6x^3+9x^2+4x+7}{2x+3}$ and $3x^2+2+\frac1{2x+3}.$

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

b) Explain why these two expressions do not represent equal numbers when $x=-\dfrac32.$

c) Show that these two expressions represent equal numbers for all $x$ other than $-\dfrac32.$