EDGE Math 8

1.	If $\frac{a}{b} = 0,$ then $a = 0.$ Use this fact and the Zero Product Principle to solve for x in the following equation:

$\frac{x^{2} + 2 x - 8}{3} = 0$

x = 4 or x = - 2

x = - 4 or x = 2

x = 8 or x = - 1

none of the choices

Answer: $x = - 4 or x = 2$

2.	Based on the same given conditions in the previous item, solve for x in the following equation:

$\frac{x^{2} - 25}{x - 1} = 0$

x = - 5 or x = 5

x = 1 or x = 25

x = 1 or x = 0

none of the choices

Answer: $x = - 5 or x = 5$

3.	Simplify the following expression:

$\frac{x^{4} - y^{4}}{x^{5} - x^{3} y^{2} + x^{2} y^{3} - y^{5}}$

\frac{x + y}{x^{2} - x y + y^{2}}

\frac{x^{2} + y^{2}}{(x + y) (x^{2} - x y + y^{2})}

\frac{x^{2} + y^{2}}{(x - y) (x^{2} + x y + y^{2})}

none of the choices

Answer: $\frac{x^{2} + y^{2}}{(x + y) (x^{2} - x y + y^{2})}$

4.	Simplify the following expression:

$\frac{a x + b x + a y + b y}{a x + 2 a y + b x + 2 b y}$

\frac{1}{2}

\frac{1}{2 y}

\frac{1}{2 x + 2 y}

none of the choices

Answer: none of the choices; the answer is $\frac{x + y}{x + 2 y}$