Complex Fractions Simplified

Adv Math: Complex Fractions

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$$\frac{\frac{2}{x^2-1}}{\frac{3}{x+1}}$$  

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$$\frac{\frac{1}{x^2-7x+12}}{\frac{2}{x-4}}$$  

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$$\frac{\frac{1}{2}+\frac{2}{3}}{\frac{5}{6}+\frac{1}{12}}$$  
Leave this answer in improper fraction form. 

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$$\frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x}-\frac{1}{y}}$$  

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$$\frac{1-\frac{3}{c+4}}{\frac{1}{c+4}+\frac{c}{3}}$$  

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$$\frac{\frac{1}{2}+\frac{1}{5}}{\frac{1}{10}+\frac{1}{5}}$$  
Leave this answer as an improper fraction

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$$\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x}+\frac{1}{y}}$$  

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

Multiple Choice

Simplify.
$$\frac{\frac{3x+2}{x^2}-\frac{3}{x^2}}{\frac{3x+2}{x^2}-\frac{3}{2}}$$  

• $$\frac{6x-2}{6x+4-3x^2}$$  

• $$\frac{29x^2+36x+12+3x^3}{27x^2+9x^5+12x^4+4x^3}$$  

• $$\frac{18x^2+8x}{24+9x}$$  

• $$\frac{-45x-30}{-12x-36x^2-16}$$  

Multiple Choice

Simplify.
$$\frac{\frac{u}{16}-\frac{9}{4}}{\frac{u^2}{16}+\frac{16}{u^2}}$$  

• $$\frac{u^3-36u^2}{u^4+256}$$  

• $$\frac{36-u^4}{225-3u^3}$$  

• $$\frac{25u+100}{3u^2-125}$$  

• $$-\frac{832u^2}{30000-75u^3}$$  

Multiple Choice

Simplify.
$$\frac{\frac{x+3}{x-5}}{\frac{5}{x+3}+\frac{5}{x-5}}$$  

• $$\frac{x-2}{x^2-2x-15}$$  

• $$\frac{5x^2-50x+125}{130-x}$$  

• $$\frac{x^2+6x+9}{10x-10}$$  

• $$\frac{x^2-2x+110}{125}$$  

Multiple Choice

Simplify.
$$\frac{\frac{x+4}{x-1}}{\frac{x+4}{x-1}+\frac{x-1}{x+2}}$$  

• $$\frac{-8-x}{x^3+10x^2+32x+32}$$  

• $$\frac{x^2+6x+8}{2x^2+4x+9}$$  

• $$\frac{2x+3}{x^2+4x+4}$$  

• $$\frac{2x^2+7x}{x^2+x-2}$$  

Multiple Choice

Simplify.
$$\frac{\frac{1}{x}}{\frac{x-1}{16}}$$  

• $$\frac{1}{x}$$  

• $$\frac{16x-16}{x^3}$$  

• $$\frac{16}{x^2-x}$$  

• $$\frac{16}{x^2}$$  

Multiple Choice

Simplify.
$$\frac{\frac{1}{3a-4}}{\frac{3a-4}{a-2}}$$  

• $$\frac{3a^3-4a^2}{a^2-4a+4}$$  

• $$\frac{a}{a-2}$$  

• $$\frac{3a-4}{a-2}$$  

• $$\frac{a-2}{9a^2-24a+16}$$