Answer Key 8.3

[latexpage]

1. \(12a^4b^5\)
2. \(25x^3y^5z\)
3. \(x(x-3)\)
4. \(4(x-2)\)
5. \((x+2)(x-4)\)
6. \(x(x-7)(x+1)\)
7. \((x+5)(x-5)\)
8. \((x+3)(x-3)^2\)
9. \((x+1)(x+2)(x+3)\)
10. \((x-5)(x-2)(x+3)\)
11. \(\begin{array}{rrl}
    \\ \\ \\ \\ \\
    \text{LCD}&=&10a^3b^2 \\ \\
    \dfrac{3a}{5b^2}\cdot \dfrac{2a^3}{2a^3} &\Rightarrow &\dfrac{6a^4}{10a^3b^2} \\ \\
    \dfrac{2}{10a^3b}\cdot \dfrac{b}{b} &\Rightarrow & \dfrac{2b}{10a^3b^2}
    \end{array}\)
12. \(\begin{array}{rrl}
    \\ \\ \\ \\ \\ \\
    \text{LCD}&=&(x-4)(x+2) \\ \\
    \dfrac{3x}{(x-4)}\cdot \dfrac{(x+2)}{(x+2)}&\Rightarrow &\dfrac{3x^2+6x}{(x-4)(x+2)} \\ \\
    \dfrac{2}{(x+2)}\cdot \dfrac{(x-4)}{(x-4)}&\Rightarrow &\dfrac{2x-8}{(x-4)(x+2)}
    \end{array}\)
13. \(\begin{array}{rrl}
    \\ \\ \\ \\ \\ \\
    \text{LCD}&=&(x-3)(x+2) \\ \\
    \dfrac{(x+2)}{(x-3)}\cdot \dfrac{(x+2)}{(x+2)}&\Rightarrow &\dfrac{x^2+4x+4}{(x-3)(x+2)} \\ \\
    \dfrac{(x-3)}{(x+2)}\cdot \dfrac{(x-3)}{(x-3)}&\Rightarrow &\dfrac{x^2-6x+9}{(x-3)(x+2)}
    \end{array}\)
14. \(\begin{array}{rrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\
    \text{LCD}&=&x(x-6) \\ \\
    \dfrac{5}{x^2-6x}&\Rightarrow &\dfrac{5}{x(x-6)} \\ \\
    \dfrac{2}{x}\cdot \dfrac{(x-6)}{(x-6)}&\Rightarrow &\dfrac{2x-12}{x(x-6)} \\ \\
    \dfrac{-3}{(x-6)}\cdot \dfrac{x}{x}&\Rightarrow & \dfrac{-3x}{x(x-6)}
    \end{array}\)
15. \(\begin{array}{rrl}
    \\ \\ \\ \\ \\ \\
    \text{LCD}&=&(x-4)^2(x+4) \\ \\
    \dfrac{x}{x^2-16}\cdot \dfrac{(x-4)}{(x-4)}&\Rightarrow &\dfrac{x^2-4x}{(x-4)^2(x+4)} \\ \\
    \dfrac{3x}{(x^2-8x+16)}\cdot \dfrac{(x+4)}{(x+4)}&\Rightarrow &\dfrac{3x^2+12}{(x-4)^2(x+4)}
    \end{array}\)
16. \(\begin{array}{rrl}
    \\ \\ \\ \\ \\ \\
    \text{LCD}&=&(x-5)(x+2) \\ \\
    \dfrac{5x+1}{x^2-3x-10}&\Rightarrow &\dfrac{5x+1}{(x-5)(x+2)} \\ \\
    \dfrac{4}{(x-5)}\cdot \dfrac{(x+2)}{(x+2)}&\Rightarrow &\dfrac{4x+8}{(x-5)(x+2)}
    \end{array}\)
17. \(\begin{array}{rrl}
    \\ \\ \\ \\ \\ \\
    \text{LCD}&=&(x+6)^2(x-6) \\ \\
    \dfrac{x+1}{x^2-36}\cdot \dfrac{(x+6)}{(x+6)}&\Rightarrow &\dfrac{x^2+7x+6}{(x+6)^2(x-6)} \\ \\
    \dfrac{(2x+3)}{(x^2+12x+36)}\cdot \dfrac{(x-6)}{(x-6)}&\Rightarrow &\dfrac{2x^2-9x-18}{(x+6)^2(x-6)}
    \end{array}\)
18. \(\begin{array}{rrl}
    \\ \\ \\ \\ \\ \\
    \text{LCD}&=&(x-4)(x+3)(x+1) \\ \\
    \dfrac{(3x+1)}{(x^2-x-12)}\cdot \dfrac{(x+1)}{(x+1)}&\Rightarrow & \dfrac{3x^2+4x+1}{(x-4)(x+3)(x+1)} \\ \\
    \dfrac{2x}{(x^2+4x+3)}\cdot \dfrac{(x-4)}{(x-4)}&\Rightarrow & \dfrac{2x^2-8x}{(x-4)(x+3)(x+1)}
    \end{array}\)
19. \(\begin{array}{rrl}
    \\ \\ \\ \\ \\ \\
    \text{LCD}&=&(x-3)(x+2) \\ \\
    \dfrac{4x}{x^2-x-6}&\Rightarrow &\dfrac{4x}{(x-3)(x+2)} \\ \\
    \dfrac{(x+2)}{(x-3)}\cdot \dfrac{(x+2)}{(x+2)}&\Rightarrow &\dfrac{x^2+4x+4}{(x-3)(x+2)}
    \end{array}\)
20. \(\begin{array}{rrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\
    \text{LCD}&=&(x-4)(x-2)(x+5) \\ \\
    \dfrac{3x}{x^2-6x+8}\cdot \dfrac{(x+5)}{(x+5)}&\Rightarrow & \dfrac{3x^2+15x}{(x-4)(x-2)(x+5)} \\ \\
    \dfrac{(x-2)}{(x^2+x-20)}\cdot \dfrac{(x-2)}{(x-2)}&\Rightarrow & \dfrac{x^2-4x+4}{(x-4)(x-2)(x+5)} \\ \\
    \dfrac{5}{(x^2+3x-10)}\cdot \dfrac{(x-4)}{(x-4)}&\Rightarrow & \dfrac{5x-20}{(x-4)(x-2)(x+5)}
    \end{array}\)