EDGE Math 8

1.	What is the LCM of $x - 5, {(x - 5)}^{2},$ and $x^{2} - 25 ?$

x^{2} - 25

(x - 5) (x - 5)

{(x - 5)}^{2} (x + 5)

(x - 5) {(x - 5)}^{2} (x^{2} - 25)

Answer: ${(x - 5)}^{2} (x + 5)$

2.	What is the LCD of $\frac{1}{4 x},$ $\frac{3}{x (x - 4)},$ and $\frac{5}{x (x + 2)} ?$

(x - 4) (x + 2)

4 x (x^{2} + 2 x - 8)

4 x (x - 4) (x + 2)

\frac{x (x - 4) (x + 2)}{4}

Answer: $4 x (x - 4) (x + 2)$

3.	What is the sum of $\frac{x}{x^{2} - 4} + \frac{2}{x^{2} + 2 x} ?$

1

\frac{1}{x - 2}

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

\frac{x^{2} + 2 x - 4}{x (x + 2) (x - 2)}

Answer: $\frac{x^{2} + 2 x - 4}{x (x + 2) (x - 2)}$

4.	What is the difference if you subtract $\frac{4}{x + 1}$ from $\frac{3}{x - 1} ?$

\frac{- x + 2}{(x - 1) (x + 1)}

\frac{- x - 1}{(x - 1) (x + 1)}

\frac{x - 7}{(x - 1) (x + 1)}

\frac{7 - x}{(x - 1) (x + 1)}

Answer: $\frac{7 - x}{(x - 1) (x + 1)}$

5.	What is the simplest form of $\frac{\frac{2}{x} + \frac{2}{y}}{\frac{4}{x} - \frac{4}{y}} ?$

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

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

\frac{2 x + y}{4 x - y}

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

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