How do you simplify #(3x^2-5x-2)/(6x^3+2x^2+3x+1)#?

1 Answer
Don't Memorise
Jun 3, 2015

#color(red)((3x^2-5x-2))/color(purple)((6x^3+2x^2+3x+1))#

  • Factorising the numerator :
    By splitting the middle term
    #color(red)(3x^2-5x-2#

#3x^2-5x-2 = 3x^2-6x + 1x -2#
# = 3x(x-2)+1(x-2)#
# = color(red)((3x+1)(x-2)#

  • Factorising the denominator:
    By grouping
    #color(purple)(6x^3+2x^2+3x+1)#

#= (6x^3+2x^2)+(3x+1)#
# = 2x^2(3x +1)+1(3x+1)#
# = color(purple)((2x^2+1) (3x +1)#

The expression becomes:
# = color(red)(cancel(3x+1)(x-2))/ color(purple)((2x^2+1) cancel(3x +1)#
# = color(red)((x-2))/ color(purple)((2x^2+1)#

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