How do you simplify #(x^2+12x+20)/(4x^2-9)*(6x^3-9x^2)/(x^3+10x^2)*(2x+3)#?

1 Answer
May 5, 2017

Answer:

#=3(x+2)#

Explanation:

#(x^2+12x+20)/(4x^2-9).(6x^3-9x^2)/(x^3+10x^2).(2x+3)#
#" "#
#=(x^2+12x+20+16-16)/(4x^2-9).(3x^2(2x-3))/(x^2(x+10)).(2x+3)#
#" "#
#=((x^2+12x+20+16)-16)/(4x^2-9).(3x^2(2x-3))/(x^2(x+10)).(2x+3)#
#" "#
#=((x^2+12x+36)-16)/(4x^2-9).(3x^2(2x-3))/(x^2(x+10)).(2x+3)#
#" "#
#=((x^2+2(6)x+6^2)-16)/(4x^2-9).(3x^2(2x-3))/(x^2(x+10)).(2x+3)#
#" "#
#=((x+6)^2-16)/(4x^2-9).(3x^2(2x-3))/(x^2(x+10)).(2x+3)#
#" "#
#=((x+6)^2-4^2)/((2x)^2-3^2).(3x^2(2x-3))/(x^2(x+10)).(2x+3)#
#" "#
Here we will apply the difference of two squares property that says:
#" "#
#color(blue)(a^2-b^2=(a-b)(a+b)#
#" "#
#=color(blue)((x+6-4)(x+6+4))/color(blue)((2x-3)(2x+3)).(3x^2(2x-3))/(x^2(x+10)).(2x+3)#
#" "#
#=((x+2)color(green)cancel((x+10)))/(color(red)cancel((2x-3))color(purple)cancel((2x+3))).(3color(brown)cancel(x^2)color(red)cancel((2x-3)))/(color(brown)cancelx^2color(green)cancel((x+10))).color(purple)cancel((2x+3))#
#" "#
#=3(x+2)#