Вправи 201 - 300 » 233 (1)

232. Спростіть вираз: 1) (b^(\a+b)/(a- b) + a^(\a-b)/(a+ b)) • (a^(〖2\〗^(a^2 ) )/b^2 + b^(〖2\〗^(b^2 ) )/a^2 – 2^(〖\a〗^2 b^2 )) : (a^4-b^4 )/(a^2 b^2 ) = (〖ab+ b〗^2+a^2- ab )/((a- b)(a+ b)) • (a^4+b^4-〖2a〗^2 b^2 )/(a^2 b^2 ) • (a^2 b^2)/(a^4-b^4 ) = (〖(a〗^2+b^2)• 〖(a〗^4-〖2a〗^2 b^4)•a^2 b^2 )/((a- b)(a+ b)• a^2 b^2• 〖(a〗^4- b^4)) = (〖(a〗^2+b^2)(a^2-b^2 )^2 )/((a- b)(a+ b) 〖(a〗^2-b^2)(a^2+b^2) ) = (a^2-b^2 )/(a^2- b^2 ) = 1; 2) (m2 – n2 – (〖4m〗^2 n-〖4mn〗^2 )/(m+ n)) : (m/(m+ n) – n/(n- m) – 2mn/(m^2-n^2 )) = ((m^2-n^(2^(\m+n) ) )/1 – (〖4m〗^2 n-〖4mn〗^2 )/(m+ n)) : (m^(\m-n)/(m+ n) + n^(\m+n)/(m- n) – 2mn/((m- n)(m+ n))) = (〖(m〗^2-n^2)(m+ n)- 〖4m〗^2 n+〖4mn〗^2 )/(m+ n) : (m^2- mn+ mn+n^2-2mn )/((m- n)(m+ n)) = ((m- n)(m+ n)(m+ n)-4mn(m- n))/(m+ n) : 〖(m- n)〗^2/((m- n)(m+ n)) = ((m- n)((〖m+ n)〗^2-4mn))/(m+ n) : (m- n)/(m+ n) = ((m- n) 〖(m〗^2+2mn+n^2-4mn) )/(m+ n) • (m+ n)/(m- n) = ((m- n) 〖(m〗^2-2mn+ n^2)•(m+ n))/((m+ n)(m- n)) = (m – n)2.