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Объяснение:

Обрезаны уcловия:

(m-n)/m^2 -(n-m)/(mn)=(n(m-n)-m(n-m))/(m^2 •n)=(n(m-n)+m(m-n))/(nm^2)=(m-n)(n+m)/(nm^2)=(m^2 -n^2)/(nm^2)

4/(c^2 -9) -2/(c^2+3c)=4/((c-3)(c+3)) -2/(c(c+3))=(4c-2(c-3))/(c(c-3)(c+3))=(4c-2c+6)/(c(c-3)(c+3))=(2c+6)/(c(c-3)(c+3))=2(c+3)/(c(c-3)(c+3))=2/(c(c-3))=2/(c^2 -3c)

42/(x^2 +7у) -6/у=(42у-6(х^2 +7у))/(у(х^2 +7у))=(42у-6х^2 -42у)/(у(х^2 +7у))=-(6х^2)/(у(х^2 +7у))=-(6х^2)/(ух^2 +7у^2)

6b/(3-b) -2b=(6b-2b(3-b))/(3-b)=(6b-6b+2b^2)/(3-b)=(2b^2)/(3-b)

1/(х+2) +2/(х^2 -2х) -4/(4-х^2)=1/(х+2) +2/(х(х-2)) +4/((х-2)(х+2))=(х(х-2)+2(х+2)+4х)/(х(х-2)(х+2))=(х^2 -2х+2х+4+4х)/(х(х-2)(х+2))=(х^2 +4х+4)/(х(х-2)(х+2))=((х+2)^2)/(х(х-2)(х+2))=(х+2)/(х(х-2))=(х+2)/(х^2 -2х)

(a+2b)/a=1 +2b/a

√3cosx + sinx = 2cos2xРазделим обе части данного уравнения на 2(√3/2)•сosx + (1/2)•sinx = cos2xsin(π/3)•cosx + cos(π/3)•sinx = cos2x

sinα•cosβ + cosα•sinβ = sin(α + β)

sin( π/3 + x ) = cos2xsin( π/3 + x ) - cos2x = 0sin( π/3 + x ) - sin( π/2 - 2x ) = 0

sinα - sinβ = 2•sin( (1/2)•(α - β) )•cos( (1/2)•(α + β) )

2•sin( (1/2)•(π/3 + x - π/2 + 2x) )•cos( (1/2)•(π/3 + x + π/2 - 2x) ) = 02•sin( (1/2)•(3x - π/6) )•cos( (1/2)•(-x + 5π/6) ) = 0Произведение равно нулю, если хотя бы один из множителей равен нулю.1) sin( (1/2)•(3x - π/6) ) = 0(1/2)•(3x - π/6) = πn3x - π/6 = 2πn3x = π/6 + 2πnx = π/18 + 2πn/3 , n ∈ Z2) cos( (1/2)•(-x + 5π/6) ) = 0(1/2)•(-x + 5π/6) = π/2 + πk- x + 5π/6 = π + 2πkx = - π/6 + 2πk , k ∈ ZОТВЕТ:  π/18 + 2πn/3 , n ∈ Z ; - π/6 + 2πk , k ∈ Z