(дробь m/m^2-2m+1 - дробь m+2/m^2+m-2) : дробь 1/(2m-2)^2. Created by vusalina. algebra-ru

(2m-2)^2...

vusalina @vusalina

July 2022 2 12 Report

(дробь m/m^2-2m+1 - дробь m+2/m^2+m-2) : дробь 1/(2m-2)^2

ATLAS

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[m/(m^2-2m+1) - (m+2)/(m^2+m-2)]:1/(2m-2)^2=

=[m/(m-1)^2 - (m+2)/(m+2)(m-1)]*4(m-1)^2/[((m-1)^2) *(m+2)]=

=[m^2+2m-m^2-m+2]*4/(m+2)=(m+2)*4/(m+2)=4

18 votes Thanks 7

ayka89

$(\frac{m}{m^2-2m+1}-\frac{m+2}{m^2+m-2}):\frac{1}{(2m-2)^2}=(\frac{m}{(m-1)^2}-\frac{m+2}{m^2-m+2m-2})\cdot\\\cdot(4m^2-8m+4)=\frac{m}{(m-1)^2}\cdot4(m-1)^2-\frac{m+2}{(m-1)(m+2)}\cdot\\\cdot4(m-1)^2=4m-4(m-1)=4(m-m+1)=4$

21 votes Thanks 10

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