Вправи 401 - 467 » 409 (4-6)

4) (x^(-1)+y^(-1) )/(x^(-1)- y^(-1) ) – (x^(-1)-y^(-1) )/(x^(-1)+y^(-1) ) = (1/x+1/y )/(1/x- 1/y) – (1/x-1/y )/(1/x+1/y ) = ((y+ x)/xy)/((y- x)/xy) – ((y- x)/xy)/((y+ x)/xy) = ((y+ x)• xy)/(xy(y- x)) – ((y- x)• xy)/(xy•(y+ x)) = (y+ x)/(y- x) – (y- x)/(y+ x) = (〖(y+ x)〗^2-〖(y- x)〗^2 )/((y- x)(y+ x)) = (y^2+2yx+x^2-〖(y〗^2-2yx+ x^2) )/(y^2- x^2 ) = (y^2+2yx+ x^2-y^2+2yx-x^2 )/(y^2- x^2 ) = 4xy/(y^2- x^2 ); 5) (n^1+ n^2+n^3+n^4 )/(n^(-1)+ n^(-2)+ n^(-3)+n^(-4) ) = (n^1+n^2+ n^3+n^4 )/(1/n+1/n^2 +1/n^3 +1/n^4 ) = (n+n^2+n^3+ n^4 )/((n^3+n^2+ n+1 )/n^4 ) = (n•(1+ n+ n^2+ n^3 )• n^4)/(n^3+n^2+ n+1 ) = n5; 6) (〖xy〗^(-9)+x^(-9) y )/(x^(-2) y^8+ x^8 y^(-2) ) = (x^(-9) y^(-9) (x^(1-(-9))+y^(1-(-9))) )/(x^(-2) y^(-2) (y^(8-(-2))+ x^(8-(-2)))) = (x^(-9) y^(-9) (x^10+y^10) )/(x^(-2) y^(-2) (y^10+ x^10)) = x–7y–7.