Question

Simplificati rapoartele : a) x² - 9x + 14 / x² - 4  b) x² + 8x + 12 / x² + 7x+ 6  c) 4 - x² / x² + 10x + 16

Answer 1

a) ( x² - 9x + 14) / x² - 4 = ( x² - 2x - 7x + 14) / x² - 4, se foloseste - 9x = - 2x -7x
  = [( x² - 2x) - ( 7x - 14)] / x² - 4
  = [ x( x - 2) - 7( x - 2)] / ( x - 2)( x + 2)
  = ( x - 2)( x - 7) / ( x - 2)( x + 2), se simplifica cu ( x - 2)
  = x - 7 / x + 2

b) ( x² + 8x + 12) / ( x² + 7x + 6)  = ( x² + 2x + 6x + 12) / ( x² + x + 6x + 6)
     = [( x² + 2x) + ( 6x + 12)] / [( x² + x) + ( 6x + 6)]
     = [ x( x + 2) + 6( x + 2)] / [ x( x + 1) + 6 ( x + 1)]
     = ( x + 2)( x + 6) / ( x + 1)( x + 6), se simplifica cu ( x + 6)
     = x + 2 / x + 1

c) ( 4 - x²) / ( x² + 10x + 16) = ( 2 - x)( 2 +x) / ( x² + 2x + 8x + 16)
     = ( 2 - x)( x + 2) / [( x²  + 2x) + ( 8x + 16)]
     = ( 2 - x)( x + 2) / [ x( x + 2) + 8( x + 2)]
     = ( 2 - x)( x + 2) / ( x + 2)( x + 8) , se simplifica cu ( x + 2)
     = 2 - x / x + 8
 Sper ca ti-am fost de ajutor!