1.1E: Exercises
- Page ID
- 121510
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- Factor completely.
- \( 216 x^3 + 125 y^3 \)
- \( 64m^4 - 27m \)
- \( 125h^2 - 216h^5 \)
- \( 64x^3 - 125 \)
- \( 108\cos^3{(x)} - 4 e^{3x} \)
- \( 9x\left( x + 1 \right)^{-3/4} + \left( x + 1 \right)^{1/4} \)
- \( -x\left( 5x - 3 \right)^{1/4} - 9\left( 5x - 3 \right)^{-3/4} \)
- \( 6x\left( 24x + 1 \right)^{5/6} - 5\left( 24x + 1 \right)^{-1/6} \)
- Simplify the expression. When applicable, completely simplify your answer into a single rational expression without negative exponents.
- \( \dfrac{\left( 24 - x^2 \right)^{1/2} + x^2\left( 24 - x^2 \right)^{-1/2}}{24 - x^2} \)
- \( \dfrac{9\left( 7 + x \right)^{1/3} - x \left( 7 + x \right)^{-2/3}}{\left( 7 + x \right)^{2/3}} \)
- \( \dfrac{14\left( 8 + x \right)^{1/2} - x \left( 8 + x \right)^{-1/2}}{x + 8} \)
- \( \dfrac{\left( 11 - 5x \right)^{1/2} + \frac{5}{7}x\left( 11 - 5x \right)^{-1/2}}{11 - 5x} \)
- Simplify the compound rational expression. When applicable, completely simplify your answer into a single rational expression without negative exponents.
- \( 15x - \dfrac{y}{\frac{x}{15y} + \frac{y}{15x}} \)
- \( 11 - \dfrac{9}{1 - \frac{1}{x}} \)
- \( 1 + \dfrac{1}{1 + \frac{1}{13 + x}} \)
- \( \dfrac{\frac{15}{5 + x + h} - \frac{15}{5 + x}}{h} \)
- \( \dfrac{\frac{14}{(x + h)^2} - \frac{14}{x^2}}{h} \)
- \( \dfrac{25x^{-2} - 4y^{-2}}{5x^{-1} + 2y^{-1}} \)
- \( \dfrac{41x^{-1} + 97y^{-1}}{(97x + 41y)^{-1}} \)
- \( \dfrac{-\frac{7}{\sqrt{x + h}} + \frac{7}{\sqrt{x}}}{h} \)
- Rationalize the numerator. When applicable, completely simplify your answer into a single rational expression without negative exponents.
- \( \sqrt{x^2 + 36} - x \)
- \( \dfrac{\sqrt{100 + h} - 10}{h} \)
- \( \dfrac{\sqrt{x} - \sqrt{x + 9h}}{h\sqrt{x}\sqrt{x + h}} \)
- Let \( x \lt \frac{5}{3} \). Simplify the expression.\[ \dfrac{|3x - 5|}{3x^2 - 23 x + 30} \nonumber \]