задали примеры помогите решить.100 баллов 1) (4x^2-y)*7y:(49x^2-y^2) 2)(7x-y)*7:(49x^2-y^2) 3)(4x^2-25y^2)*(1:(2x+5y)+1:(2x-5y)) 4)(2x^2+xy-6y^2):(3y-2x). Created by Владимир436. algebra-ru

задали примеры помогите решить.100 баллов 1) (4x^2-y)*7y:(49x^2-y^2) 2)(7x-y)*7:...

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$1)\; \; \frac{(7x-y)\cdot 7y}{49x^2-y^2} = \frac{(7x-y)\cdot 7y}{(7x-y)(7x+y)} = \frac{7y}{7x+y} \\\\2)\; \; \frac{4x}{7y+2x}-\frac{2x-7y}{2x+7y} = \frac{4x-2x+7y}{7y+2x} = \frac{2x+7y}{7y+2x} =1\\\\3)\; \; (4x^2-25y^2)\cdot \Big ( \frac{1}{2x+5y} +\frac{1}{2x-5y} \Big )=\\\\=(2x-5y)(2x+5y)\cdot \frac{2x-5y+2x+5y}{(2x+5y)(2x-5y)} =4x$

$4)\; \; \frac{2x^2+xy-6y^2}{3y-2x}= \frac{2x^2-3xy+4xy-6y^2}{3y-2x} = \frac{-x(3y-2x)-2y(2x-3y-2x)}{3y-2x} =\\\\= \frac{(3y-2x)(-x-2y)}{3y-2x} =-x-2y$

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(7x-y)*7y:(49x^2-y^2) = (7x-y)*7y/49x^2-y^2 = (7x-y)*7y/(7x-y)*(7x+y) = 7y/7x+y

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4x:(7y+2x)-(2x-7y):(2x+7y)= 4x/2x+7y - 2x-7y/2x+7y = 4x-(2x-7y)/2x+7y = 4x-2x+7y/2x+7y = 2x+7y/2x+7y = 1

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(4x^2-25y^2)*(1:(2x+5y)+1:(2x-5y)) = (2x-5y) * (2x+5y) * (1/2x+5y + 1/ 2x-5y) = (2x-5y) * (2x+5y) * 2x-5y+2x+5y/ (2x+5y)*(2x-5y)= 4x

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(2x^2+xy-6y^2)/(3y-2x)=2x^2-3xy+4xy-6y^2/3y-2x = -x(3y-2x)-2y(2x-3y-2x)/3y-2x = (3y-2x)(-x-2y)/3y-2x = -x-2y

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