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№1.
![frac{8a^2b}{9c} * frac{3bc^3}{4a^3b} = frac{8*3*a^2b^2c^3}{9*4*a^3bc} = frac{2bc^2}{3a} = frac{2}{3}a^{-1}bc^2 \ \
frac{4-x}{x-3} - frac{x+2}{3-x} = frac{4-x}{x-3} - frac{x+2}{-(x-3) } = frac{4-x}{x-3} + frac{x+2}{x-3} = frac{4-x+x+2}{x-3} = frac{6}{x-3}](https://tex.z-dn.net/?f=+frac%7B8a%5E2b%7D%7B9c%7D++%2A++frac%7B3bc%5E3%7D%7B4a%5E3b%7D+%3D++frac%7B8%2A3%2Aa%5E2b%5E2c%5E3%7D%7B9%2A4%2Aa%5E3bc%7D+%3D++frac%7B2bc%5E2%7D%7B3a%7D+%3D++frac%7B2%7D%7B3%7Da%5E%7B-1%7Dbc%5E2+%5C++%5C+%0A+frac%7B4-x%7D%7Bx-3%7D+-+frac%7Bx%2B2%7D%7B3-x%7D+%3D++frac%7B4-x%7D%7Bx-3%7D+-++frac%7Bx%2B2%7D%7B-%28x-3%29+%7D+%3D++frac%7B4-x%7D%7Bx-3%7D+%2B+frac%7Bx%2B2%7D%7Bx-3%7D+%3D+frac%7B4-x%2Bx%2B2%7D%7Bx-3%7D+%3D++frac%7B6%7D%7Bx-3%7D+ "frac{8a^2b}{9c} * frac{3bc^3}{4a^3b} = frac{8*3*a^2b^2c^3}{9*4*a^3bc} = frac{2bc^2}{3a} = frac{2}{3}a^{-1}bc^2 \ \
frac{4-x}{x-3} - frac{x+2}{3-x} = frac{4-x}{x-3} - frac{x+2}{-(x-3) } = frac{4-x}{x-3} + frac{x+2}{x-3} = frac{4-x+x+2}{x-3} = frac{6}{x-3}")
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№3.
![frac{ab+b^2}{7a} : frac{b^2}{14a} = frac{b(a+b)}{7a} * frac{14a}{b^2} = frac{(a+b)*2}{1*b} = frac{2a+2b}{b} = frac{2a}{b} + frac{2b}{b} = frac{2a}{b} +2 \ \ \
frac{1-x^2}{x^2y } + frac{2y^2-1}{y^3} = frac{y^2(1-x^2) + x^2(2y^2-1)}{x^2y^3} = frac{y^2-x^2y^2+2x^2y^2-x^2}{x^2y^3} = frac{y^2+x^2y^2 -x^2}{x^2y^3} = \ \
= frac{y^2}{x^2y^3} + frac{x^2y^2}{x^2y^3} - frac{x^2}{x^2y^3} = frac{1}{x^2y} + frac{1}{y} - frac{1}{y^3}](https://tex.z-dn.net/?f=+frac%7Bab%2Bb%5E2%7D%7B7a%7D+%3A++frac%7Bb%5E2%7D%7B14a%7D+%3D++frac%7Bb%28a%2Bb%29%7D%7B7a%7D+%2A+frac%7B14a%7D%7Bb%5E2%7D+%3D++frac%7B%28a%2Bb%29%2A2%7D%7B1%2Ab%7D+%3D++frac%7B2a%2B2b%7D%7Bb%7D+%3D++frac%7B2a%7D%7Bb%7D+%2B+frac%7B2b%7D%7Bb%7D+%3D++frac%7B2a%7D%7Bb%7D+%2B2+%5C++%5C++%5C+%0A+frac%7B1-x%5E2%7D%7Bx%5E2y+%7D+%2B+frac%7B2y%5E2-1%7D%7By%5E3%7D+%3D++frac%7By%5E2%281-x%5E2%29+%2B+x%5E2%282y%5E2-1%29%7D%7Bx%5E2y%5E3%7D+%3D+frac%7By%5E2-x%5E2y%5E2%2B2x%5E2y%5E2-x%5E2%7D%7Bx%5E2y%5E3%7D+%3D++frac%7By%5E2%2Bx%5E2y%5E2+-x%5E2%7D%7Bx%5E2y%5E3%7D+%3D++%5C++%5C+%0A%3D+frac%7By%5E2%7D%7Bx%5E2y%5E3%7D+%2B+frac%7Bx%5E2y%5E2%7D%7Bx%5E2y%5E3%7D+-+frac%7Bx%5E2%7D%7Bx%5E2y%5E3%7D+%3D++frac%7B1%7D%7Bx%5E2y%7D+%2B+frac%7B1%7D%7By%7D+-+frac%7B1%7D%7By%5E3%7D+ "frac{ab+b^2}{7a} : frac{b^2}{14a} = frac{b(a+b)}{7a} * frac{14a}{b^2} = frac{(a+b)*2}{1*b} = frac{2a+2b}{b} = frac{2a}{b} + frac{2b}{b} = frac{2a}{b} +2 \ \ \
frac{1-x^2}{x^2y } + frac{2y^2-1}{y^3} = frac{y^2(1-x^2) + x^2(2y^2-1)}{x^2y^3} = frac{y^2-x^2y^2+2x^2y^2-x^2}{x^2y^3} = frac{y^2+x^2y^2 -x^2}{x^2y^3} = \ \
= frac{y^2}{x^2y^3} + frac{x^2y^2}{x^2y^3} - frac{x^2}{x^2y^3} = frac{1}{x^2y} + frac{1}{y} - frac{1}{y^3}")
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