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![frac{a-3}{a+3}+ frac{a+2}{a-2}= frac{(a-3)(a-2)-(a+3)(a+2)}{(a+3)(a-2)} = frac{a^2-2a-3a+6-(a^2+2a+3a+6)}{a^2-2a+3a-6} = frac{a-3}{a+3}+ frac{a+2}{a-2}= frac{(a-3)(a-2)-(a+3)(a+2)}{(a+3)(a-2)} = frac{a^2-2a-3a+6-(a^2+2a+3a+6)}{a^2-2a+3a-6} =](https://tex.z-dn.net/?f=+frac%7Ba-3%7D%7Ba%2B3%7D%2B+frac%7Ba%2B2%7D%7Ba-2%7D%3D+frac%7B%28a-3%29%28a-2%29-%28a%2B3%29%28a%2B2%29%7D%7B%28a%2B3%29%28a-2%29%7D+%3D+frac%7Ba%5E2-2a-3a%2B6-%28a%5E2%2B2a%2B3a%2B6%29%7D%7Ba%5E2-2a%2B3a-6%7D+%3D+)
![=frac{-10a}{a^2+a-6} = -frac{10a}{a^2+a-6} . =frac{-10a}{a^2+a-6} = -frac{10a}{a^2+a-6} .](https://tex.z-dn.net/?f=%3Dfrac%7B-10a%7D%7Ba%5E2%2Ba-6%7D+%3D+-frac%7B10a%7D%7Ba%5E2%2Ba-6%7D+.)
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![frac{p+2}{p+1} - frac{p+6}{p-3} = frac{(p+2)(p-3)-(p+6)(p+1)}{(p+1)(p-3)} = frac{p^2-p-6-(p^2+7p+6)}{p^2-2p-3} = -frac{8p}{p^2-2p-3} frac{p+2}{p+1} - frac{p+6}{p-3} = frac{(p+2)(p-3)-(p+6)(p+1)}{(p+1)(p-3)} = frac{p^2-p-6-(p^2+7p+6)}{p^2-2p-3} = -frac{8p}{p^2-2p-3}](https://tex.z-dn.net/?f=+frac%7Bp%2B2%7D%7Bp%2B1%7D+-+frac%7Bp%2B6%7D%7Bp-3%7D+%3D+frac%7B%28p%2B2%29%28p-3%29-%28p%2B6%29%28p%2B1%29%7D%7B%28p%2B1%29%28p-3%29%7D+%3D+frac%7Bp%5E2-p-6-%28p%5E2%2B7p%2B6%29%7D%7Bp%5E2-2p-3%7D+%3D+-frac%7B8p%7D%7Bp%5E2-2p-3%7D+)
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![frac{1}{5y}*( frac{x+4y}{x+y}- frac{x-y}{x-4y} )= frac{1}{5y}* frac{(x+4y)(x-4y)-(x-y)(x+y)}{(x+y)(x-4y)} = frac{1}{5y}*( frac{x+4y}{x+y}- frac{x-y}{x-4y} )= frac{1}{5y}* frac{(x+4y)(x-4y)-(x-y)(x+y)}{(x+y)(x-4y)} =](https://tex.z-dn.net/?f=+frac%7B1%7D%7B5y%7D%2A%28+frac%7Bx%2B4y%7D%7Bx%2By%7D-+frac%7Bx-y%7D%7Bx-4y%7D++%29%3D+frac%7B1%7D%7B5y%7D%2A+frac%7B%28x%2B4y%29%28x-4y%29-%28x-y%29%28x%2By%29%7D%7B%28x%2By%29%28x-4y%29%7D+%3D)
![= frac{1}{5y} * frac{x^2-(4y)^2-(x^2-y^2)}{x^2-4xy+yx-4y^2} = frac{1}{5y} * frac{-15y^2}{x^2-3xy-4y^2} =- frac{3y}{x^2-3xy-4y^2} = frac{1}{5y} * frac{x^2-(4y)^2-(x^2-y^2)}{x^2-4xy+yx-4y^2} = frac{1}{5y} * frac{-15y^2}{x^2-3xy-4y^2} =- frac{3y}{x^2-3xy-4y^2}](https://tex.z-dn.net/?f=%3D+frac%7B1%7D%7B5y%7D+%2A+frac%7Bx%5E2-%284y%29%5E2-%28x%5E2-y%5E2%29%7D%7Bx%5E2-4xy%2Byx-4y%5E2%7D+%3D+frac%7B1%7D%7B5y%7D+%2A+frac%7B-15y%5E2%7D%7Bx%5E2-3xy-4y%5E2%7D+%3D-+frac%7B3y%7D%7Bx%5E2-3xy-4y%5E2%7D+)
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![frac{1}{3c} *( frac{d-c}{2c+d} + frac{2c-d}{c+d} )= frac{1}{3c} * frac{(d-c)(d+c)+(2c-d)(2c+d)}{(2c+d)(c+d)} = frac{1}{3c}* frac{d^2-c^2+4c^2-d^2}{2c^2+3cd+d^2} = frac{1}{3c} *( frac{d-c}{2c+d} + frac{2c-d}{c+d} )= frac{1}{3c} * frac{(d-c)(d+c)+(2c-d)(2c+d)}{(2c+d)(c+d)} = frac{1}{3c}* frac{d^2-c^2+4c^2-d^2}{2c^2+3cd+d^2} =](https://tex.z-dn.net/?f=+frac%7B1%7D%7B3c%7D+%2A%28+frac%7Bd-c%7D%7B2c%2Bd%7D+%2B+frac%7B2c-d%7D%7Bc%2Bd%7D+%29%3D+frac%7B1%7D%7B3c%7D+%2A+frac%7B%28d-c%29%28d%2Bc%29%2B%282c-d%29%282c%2Bd%29%7D%7B%282c%2Bd%29%28c%2Bd%29%7D+%3D+frac%7B1%7D%7B3c%7D%2A+frac%7Bd%5E2-c%5E2%2B4c%5E2-d%5E2%7D%7B2c%5E2%2B3cd%2Bd%5E2%7D+%3D)
![=frac{1}{3c}* frac{3c^2}{2c^2+3cd+d^2}= frac{c}{2c^2+3cd+d^2} =frac{1}{3c}* frac{3c^2}{2c^2+3cd+d^2}= frac{c}{2c^2+3cd+d^2}](https://tex.z-dn.net/?f=%3Dfrac%7B1%7D%7B3c%7D%2A+frac%7B3c%5E2%7D%7B2c%5E2%2B3cd%2Bd%5E2%7D%3D+frac%7Bc%7D%7B2c%5E2%2B3cd%2Bd%5E2%7D+)
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