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1) ![frac{y+2xy}{x^2-y}|_{x=0,y=-1}= frac{-1+2*0*(-1)}{0^2-(-1)}=frac{-1}{1}=-1 frac{y+2xy}{x^2-y}|_{x=0,y=-1}= frac{-1+2*0*(-1)}{0^2-(-1)}=frac{-1}{1}=-1](https://tex.z-dn.net/?f=frac%7By%2B2xy%7D%7Bx%5E2-y%7D%7C_%7Bx%3D0%2Cy%3D-1%7D%3D+frac%7B-1%2B2%2A0%2A%28-1%29%7D%7B0%5E2-%28-1%29%7D%3Dfrac%7B-1%7D%7B1%7D%3D-1)
2)![frac{a}{a+2b},and,frac{-2b}{2b-a} frac{a}{a+2b},and,frac{-2b}{2b-a}](https://tex.z-dn.net/?f=frac%7Ba%7D%7Ba%2B2b%7D%2Cand%2Cfrac%7B-2b%7D%7B2b-a%7D)
![frac{a}{a+2b}* frac{a-2b}{a-2b},and,frac{2b}{-(2b-a)}*frac{a+2b}{a+2b} frac{a}{a+2b}* frac{a-2b}{a-2b},and,frac{2b}{-(2b-a)}*frac{a+2b}{a+2b}](https://tex.z-dn.net/?f=frac%7Ba%7D%7Ba%2B2b%7D%2A+frac%7Ba-2b%7D%7Ba-2b%7D%2Cand%2Cfrac%7B2b%7D%7B-%282b-a%29%7D%2Afrac%7Ba%2B2b%7D%7Ba%2B2b%7D)
![frac{a(a-2b)}{(a+2b)(a-2b)},and,frac{2b(a+2b)}{-(2b-a)(a+2b)} frac{a(a-2b)}{(a+2b)(a-2b)},and,frac{2b(a+2b)}{-(2b-a)(a+2b)}](https://tex.z-dn.net/?f=frac%7Ba%28a-2b%29%7D%7B%28a%2B2b%29%28a-2b%29%7D%2Cand%2Cfrac%7B2b%28a%2B2b%29%7D%7B-%282b-a%29%28a%2B2b%29%7D)
![frac{a(a-2b)}{(a+2b)(a-2b)},and,frac{2b(a+2b)}{(a-2b)(a+2b)} frac{a(a-2b)}{(a+2b)(a-2b)},and,frac{2b(a+2b)}{(a-2b)(a+2b)}](https://tex.z-dn.net/?f=frac%7Ba%28a-2b%29%7D%7B%28a%2B2b%29%28a-2b%29%7D%2Cand%2Cfrac%7B2b%28a%2B2b%29%7D%7B%28a-2b%29%28a%2B2b%29%7D)
3)![2frac{1}{4}a^{-1}b^3*(frac{2}{9}a^2b^{-3})=<br />frac{2*4+1}{4}* frac{2}{9}*a^{-1}*a^2*b^3*b^{-3}= 2frac{1}{4}a^{-1}b^3*(frac{2}{9}a^2b^{-3})=<br />frac{2*4+1}{4}* frac{2}{9}*a^{-1}*a^2*b^3*b^{-3}=](https://tex.z-dn.net/?f=2frac%7B1%7D%7B4%7Da%5E%7B-1%7Db%5E3%2A%28frac%7B2%7D%7B9%7Da%5E2b%5E%7B-3%7D%29%3D%26lt%3Bbr+%2F%26gt%3Bfrac%7B2%2A4%2B1%7D%7B4%7D%2A+frac%7B2%7D%7B9%7D%2Aa%5E%7B-1%7D%2Aa%5E2%2Ab%5E3%2Ab%5E%7B-3%7D%3D)
![=frac{9}{4}* frac{2}{9}*a^{-1+2}*b^{3+(-3)}=frac{2}{4}*a^1*b^0=0.5a=frac{a}{2} =frac{9}{4}* frac{2}{9}*a^{-1+2}*b^{3+(-3)}=frac{2}{4}*a^1*b^0=0.5a=frac{a}{2}](https://tex.z-dn.net/?f=%3Dfrac%7B9%7D%7B4%7D%2A+frac%7B2%7D%7B9%7D%2Aa%5E%7B-1%2B2%7D%2Ab%5E%7B3%2B%28-3%29%7D%3Dfrac%7B2%7D%7B4%7D%2Aa%5E1%2Ab%5E0%3D0.5a%3Dfrac%7Ba%7D%7B2%7D)
4)![frac{2x}{3}:frac{3}{2x}*frac{9}{4xy}:frac{x}{2y}=(frac{2x}{3}:frac{3}{2x})*frac{9}{4xy}:frac{x}{2y}=(frac{2x}{3}*frac{2x}{3})*frac{9}{4xy}:frac{x}{2y}= frac{2x}{3}:frac{3}{2x}*frac{9}{4xy}:frac{x}{2y}=(frac{2x}{3}:frac{3}{2x})*frac{9}{4xy}:frac{x}{2y}=(frac{2x}{3}*frac{2x}{3})*frac{9}{4xy}:frac{x}{2y}=](https://tex.z-dn.net/?f=frac%7B2x%7D%7B3%7D%3Afrac%7B3%7D%7B2x%7D%2Afrac%7B9%7D%7B4xy%7D%3Afrac%7Bx%7D%7B2y%7D%3D%28frac%7B2x%7D%7B3%7D%3Afrac%7B3%7D%7B2x%7D%29%2Afrac%7B9%7D%7B4xy%7D%3Afrac%7Bx%7D%7B2y%7D%3D%28frac%7B2x%7D%7B3%7D%2Afrac%7B2x%7D%7B3%7D%29%2Afrac%7B9%7D%7B4xy%7D%3Afrac%7Bx%7D%7B2y%7D%3D)
![=frac{2x*2x*9}{3*3*4xy}:frac{x}{2y}=frac{4x^2*9}{9*4xy}*frac{2y}{x}=frac{4x^2}{4xy}*frac{2y}{x}=frac{4x^2y*2}{4x^2y}=2 =frac{2x*2x*9}{3*3*4xy}:frac{x}{2y}=frac{4x^2*9}{9*4xy}*frac{2y}{x}=frac{4x^2}{4xy}*frac{2y}{x}=frac{4x^2y*2}{4x^2y}=2](https://tex.z-dn.net/?f=%3Dfrac%7B2x%2A2x%2A9%7D%7B3%2A3%2A4xy%7D%3Afrac%7Bx%7D%7B2y%7D%3Dfrac%7B4x%5E2%2A9%7D%7B9%2A4xy%7D%2Afrac%7B2y%7D%7Bx%7D%3Dfrac%7B4x%5E2%7D%7B4xy%7D%2Afrac%7B2y%7D%7Bx%7D%3Dfrac%7B4x%5E2y%2A2%7D%7B4x%5E2y%7D%3D2)
5)![frac{1-x}{2}+frac{2+3x}{5}+frac{x}{6}=frac{1}{30} frac{1-x}{2}+frac{2+3x}{5}+frac{x}{6}=frac{1}{30}](https://tex.z-dn.net/?f=frac%7B1-x%7D%7B2%7D%2Bfrac%7B2%2B3x%7D%7B5%7D%2Bfrac%7Bx%7D%7B6%7D%3Dfrac%7B1%7D%7B30%7D)
![frac{(1-x)*15}{2*15}+frac{(2+3x)*6}{5*6}+frac{x*5}{6*5}=frac{1}{30} frac{(1-x)*15}{2*15}+frac{(2+3x)*6}{5*6}+frac{x*5}{6*5}=frac{1}{30}](https://tex.z-dn.net/?f=frac%7B%281-x%29%2A15%7D%7B2%2A15%7D%2Bfrac%7B%282%2B3x%29%2A6%7D%7B5%2A6%7D%2Bfrac%7Bx%2A5%7D%7B6%2A5%7D%3Dfrac%7B1%7D%7B30%7D)
![15(1-x)+6(2+3x)+5x=1 15(1-x)+6(2+3x)+5x=1](https://tex.z-dn.net/?f=15%281-x%29%2B6%282%2B3x%29%2B5x%3D1)
![15-15x+12+18x+5x=1 15-15x+12+18x+5x=1](https://tex.z-dn.net/?f=15-15x%2B12%2B18x%2B5x%3D1)
![8x=-26 8x=-26](https://tex.z-dn.net/?f=8x%3D-26)
![2*4x=2*13 2*4x=2*13](https://tex.z-dn.net/?f=2%2A4x%3D2%2A13)
![4x=13 4x=13](https://tex.z-dn.net/?f=4x%3D13)
![x=frac{13}{4} x=frac{13}{4}](https://tex.z-dn.net/?f=x%3Dfrac%7B13%7D%7B4%7D)
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