Question

Resolva as expressões a seguir.
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Answer 1

c)    [ 2 - (x + y) ÷ (x - y) ] ÷ [ (x - y) ÷ (x + y) - 2 ] =

   = [ 2(x - y) ÷ (x - y) - (x + y) ÷ (x - y) ] ÷ [ (x - y) ÷ (x + y) - 2(x + y) ÷ (x + y) ] =

   = [ (2(x - y) - (x + y)) ÷ (x - y) ] ÷ [ ((x - y) - 2(x + y)) ÷ (x + y) ] =

   = [ (2x - 2y - x - y) ÷ (x - y) ] ÷ [ (x - y - 2x - 2y) ÷ (x + y) ] =

   = [ (x - 3y) ÷ (x - y) ] ÷ [ (-x - 3y) ÷ (x + y) ] =

   = (x - 3y)(x + y) ÷ (x - y)(-x - 3y)

d)    [ x + y ÷ z ] ÷ [ (x²z² - y²) ÷ z ] =

   = [ xz ÷ z + y ÷ z ] ÷ [ (x²z² - y²) ÷ z ] =

   = [ xz + y ÷ z ] ÷ [ (x²z² - y²) ÷ z ] =

   = [ xz + y ] ÷ [ (x²z² - y²) ] =

   = [ xz + y ] ÷ [ (xz - y)(xz + y) ] =

   = 1 ÷ (xz - y)

e)    [ (5x² + 5y²) ÷ (x² + 2xy + y²) ] ÷ [ (3x² + 3y²) ÷ (x² - y²) ] =

   = [ 5(x² + y²) ÷ (x + y)² ] ÷ [ 3(x² + y²) ÷ (x² - y²) ] =

   = 5(x² + y²)(x² - y²) ÷ 3(x² + y²)(x + y)² =

   = 5(x² - y²) ÷ 3(x + y)² =

   = 5(x - y)(x + y) ÷ 3(x + y)² =

   = 5(x - y) ÷ 3(x + y)

f)     [ 2 / (x + 3) - 3 / (x - 3) ] / [ 5 / (x² - 9) ] =

   = [ 2(x - 3) ÷ (x + 3)(x - 3) - 3(x + 3) ÷ (x - 3)(x + 3) ] ÷ [ 5 ÷ (x² - 9) ] =

   = [ 2(x - 3) ÷ (x² - 3²) - 3(x + 3) ÷ (x² - 3²) ] ÷ [ 5 ÷ (x² - 9) ] =

   = [ (2x - 6) ÷ (x² - 9) - (3x + 9) ÷ (x² - 9) ] ÷ [ 5 ÷ (x² - 9) ] =

   = [ (2x - 6) - (3x + 9) ÷ (x² - 9) ] ÷ [ 5 ÷ (x² - 9) ] =

   = (2x - 6 - 3x - 9) ÷ 5 =

   = (-x - 15) ÷ 5