Question

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

Answer 1

[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

Answer 2

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