SAT Question d8789a4c: Equivalent Expressions answer and explanation with Desmos solution

Choice B is incorrect. This value of $c$ does not produce a difference of squares. When $6$ is substituted for $c$ in the given expression, the result is $\frac{x^2-6}{x-b}$. The expression $x^2-6$ can't be factored with integer values, and therefore $\frac{x^2-6}{x-b}$ isn't equivalent to $x+b$.

Choice C is incorrect. This value of $c$ does not produce a difference of squares. When $8$ is substituted for $c$ in the given expression, the result is $\frac{x^2-8}{x-b}$. The expression $x^2-8$ can't be factored with integer values, and therefore $\frac{x^2-8}{x-b}$ isn't equivalent to $x+b$.

Choice D is incorrect. This value of $c$ does not produce a difference of squares. When $10$ is substituted for $c$ in the given expression, the result is $\frac{x^2-10}{x-b}$. The expression $x^2-10$ can't be factored with integer values, and therefore $\frac{x^2-10}{x-b}$ isn't equivalent to $x+b$.