以下三道分式题目...希望有讲解,
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以下三道分式题目...希望有讲解,
![](http://img.wesiedu.com/upload/7/a7/7a7f648418f638fc5d0a5d653ff390c5.jpg)
![](http://img.wesiedu.com/upload/7/a7/7a7f648418f638fc5d0a5d653ff390c5.jpg)
![以下三道分式题目...希望有讲解,](/uploads/image/z/8663081-41-1.jpg?t=%E4%BB%A5%E4%B8%8B%E4%B8%89%E9%81%93%E5%88%86%E5%BC%8F%E9%A2%98%E7%9B%AE...%E5%B8%8C%E6%9C%9B%E6%9C%89%E8%AE%B2%E8%A7%A3%2C)
17.∵3x-4y=0,则y=3x/4.(1)
∴(1)(3x-y)/(2x+5y)
=(3x-3x/4)/(2x+15x/4) (把(1)式代入)
=(9x/4)/(23x/4)
=9/23;
(2)(x^2+2xy)/(2x^2-y^2)
=(x^2+3x^2/2)/(2x^2-9x^2/16) (把(1)式代入)
=(5x^2/2)/(23x^2/16)
=40/23;
(3)(xy^2-x^2y)/(2x^3+3y^3)
=(9x^3/16-3x^3/4)/(2x^3+81x^3/64) (把(1)式代入)
=(-3x^3/16)/(209x^3/64)
=-12/209.
18.∵1/x-1/y=5,则y-x=5xy.(1)
∴(-x+xy+y)/(2x+7xy-2y)
=(xy+(y-x))/(7xy-2(y-x))
=(xy+5xy)/(7xy-10xy) (把(1)式代入)
=(6xy)/(-3xy)
=-2.
19.∵设x/2=y/3=z/4=t,则x=2t,y=3t,z=4t.(1)
∴(xy+yz+zx)/(x^2+y^2+z^2)
=(6t^2+12t^2+8t^2)/(4t^2+9t^2+16t^2) (把(1)式代入)
=(26t^2)/(29t^2)
=26/29.
∴(1)(3x-y)/(2x+5y)
=(3x-3x/4)/(2x+15x/4) (把(1)式代入)
=(9x/4)/(23x/4)
=9/23;
(2)(x^2+2xy)/(2x^2-y^2)
=(x^2+3x^2/2)/(2x^2-9x^2/16) (把(1)式代入)
=(5x^2/2)/(23x^2/16)
=40/23;
(3)(xy^2-x^2y)/(2x^3+3y^3)
=(9x^3/16-3x^3/4)/(2x^3+81x^3/64) (把(1)式代入)
=(-3x^3/16)/(209x^3/64)
=-12/209.
18.∵1/x-1/y=5,则y-x=5xy.(1)
∴(-x+xy+y)/(2x+7xy-2y)
=(xy+(y-x))/(7xy-2(y-x))
=(xy+5xy)/(7xy-10xy) (把(1)式代入)
=(6xy)/(-3xy)
=-2.
19.∵设x/2=y/3=z/4=t,则x=2t,y=3t,z=4t.(1)
∴(xy+yz+zx)/(x^2+y^2+z^2)
=(6t^2+12t^2+8t^2)/(4t^2+9t^2+16t^2) (把(1)式代入)
=(26t^2)/(29t^2)
=26/29.