Question

Решите 55,56 и 57
Даю 25 баллов

Answer 1

$\displaystyle\bf\\55)\\\\\frac{y^{2}-x^{2} }{2xy} :\frac{x+y}{2y}=\frac{(y-x)\cdot(y+x)}{2xy}\cdot\frac{2y}{x+y}=\frac{y-x}{x} \\\\\\Otvet \ : \ C)\\\\56)\\\\1)\\\\\frac{1}{m^{2}-m } -\frac{1}{m-1}= \frac{1}{m\cdot(m-1) } -\frac{1}{m-1}= \\\\\\=\frac{1-m}{m\cdot(m-1)} =-\frac{1}{m} \\\\2)\\\\-\frac{1}{m} \cdot\frac{m}{m+2} =-\frac{1}{m+2} \\\\3)\\\\-\frac{1}{m+2}+\frac{m+1}{m+2} =\frac{-1+m+1}{m+2} =\frac{m}{m+2} \\\\\\Otvet \ . \ C)$

$\displaystyle\bf\\57)\\\\\frac{4x^{2} -4xy+3y^{2} }{2y^2+2xy-5x^{2} } =1\\\\\\4x^{2} -4xy+3y^{2} =2y^{2} +2xy-5x^{2} \\\\4x^{2} -4xy+3y^{2} -2y^{2} -2xy+5x^{2}=0\\\\9x^{2} -6xy+y^{2} =0\\\\(3x-y)^{2} =0\\\\3x-y=0\\\\y=3x\\\\\\\frac{4x-y}{4x+y}=\frac{4x-3x}{4x+3x}=\frac{x}{7x}=\frac{1}{7} \\\\\\Otvet \ : \ B)$