Вправи 101 - 200 » 165 (6-10)

6) (5^(\m+n)/(m-n) – 4^(\m-n)/(m+n)) : (m+9n)/(m+n) = (5(m+n)- 4(m-n))/((m-n)(m+n)) • (m+n)/(m+9n) = (5m+5n-4m+4n)/((m-n)(m+n)) • (m+n)/(m+9n) = ((m+9n) • (m+n))/((m-n)(m+n)(m+9n)) = 1/(m-n); 7) (x-2)/(x+2) • (x\x–2 – x^2/(x-2)) = (x-2)/(x+2) • (x(x-2)- x^2)/(x-2)= ((x-2)(x^2- 2x- x^2))/((x+2)(x-2)) = (-2x)/(x+2) = –2x/(x+2); 8) (x^2+ x)/4 : x^2/4 + (x-1)/x = (x(x+1)•4)/(4 • x^2 ) + (x-1)/x = (x+1)/x + (x-1)/x = (x+1+x-1)/x = 2x/x = 2; 9) (6c^2)/(c^2- 1) : (1/(c-1) + 1\c–1) = (6c^2)/((c-1)(c+1)) : (1+c-1)/(c-1) = (6c^2•(c-1) )/((c-1)(c+1)•c) = 6c/(c+1); 10) (x^(\x-y)/(x+y) + y^(\x+y)/(x-y)) • (x^2+ xy)/(x^2+ y^2 ) = (x(x-y)+ y(x+y))/((x+y)(x-y)) • (x(x+y))/(x^2+ y^2 ) = (x^2- xy+xy+ y^2)/((x+y)(x-y)) • (x(x+y))/(x^2+ y^2 ) = ((x^2+ y^2 ) • x(x+y))/((x+y)(x-y)(x^2+ y^2)) = x/(x-y).