How do you simplify #(x-2)/(5x(x-1)) + 1/(x-1) - (3x+2)/(x^2+4x-5)#?

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Answer 1 · 2018-03-23T12:32:41

#= (15 - 9x^2 - 7x)/(5x^3 + 20x^2 - 25x)#

#color(white)(xx)(x - 2)/(5x(x -1)) + 1/(x - 1) - (3x + 2)/(x^2 + 4x - 5)#

#= (x - 2)/(5x(x -1)) + 1/(x - 1) - (3x + 2)/(x^2 - x +5x - 5)#

[Broken up #4x# as #-x + 5x#]

#=(x - 2)/(5x(x -1)) + 1/(x - 1) - (3x + 2)/(x(x - 1) + 5(x - 1))#

#=(x - 2)/(5x(x -1)) + 1/(x - 1) - (3x + 2)/((x-1)(x+5))#

#=((x - 2)(x + 5) + 5x(x + 5) -5x(3x + 2))/(5x(x-1)(x+5))# [Taking The LCM]

#=((x^2 - 2x + 5x - 10) + (5x^2 + 25) -(15x^2 + 10x))/(5x(x-1)(x+5))#

#= (x^2 - 2x + 5x - 10 + 5x^2 + 25 -15x^2 - 10x)/(5x(x-1)(x+5))#

#= (-9x^2 - 7x + 15)/(5x^3 + 20x^2 - 25x)#

#= (15 - 9x^2 - 7x)/(5x^3 + 20x^2 - 25x)#

Hope this helps.