How do you simplify (x^2+12x+20)/(4x^2-9)*(6x^3-9x^2)/(x^3+10x^2)*(2x+3)x2+12x+204x296x39x2x3+10x2(2x+3)?

1 Answer
May 5, 2017

=3(x+2)=3(x+2)

Explanation:

(x^2+12x+20)/(4x^2-9).(6x^3-9x^2)/(x^3+10x^2).(2x+3)x2+12x+204x29.6x39x2x3+10x2.(2x+3)
" "
=(x^2+12x+20+16-16)/(4x^2-9).(3x^2(2x-3))/(x^2(x+10)).(2x+3)=x2+12x+20+16164x29.3x2(2x3)x2(x+10).(2x+3)
" "
=((x^2+12x+20+16)-16)/(4x^2-9).(3x^2(2x-3))/(x^2(x+10)).(2x+3)=(x2+12x+20+16)164x29.3x2(2x3)x2(x+10).(2x+3)
" "
=((x^2+12x+36)-16)/(4x^2-9).(3x^2(2x-3))/(x^2(x+10)).(2x+3)=(x2+12x+36)164x29.3x2(2x3)x2(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)=(x2+2(6)x+62)164x29.3x2(2x3)x2(x+10).(2x+3)
" "
=((x+6)^2-16)/(4x^2-9).(3x^2(2x-3))/(x^2(x+10)).(2x+3)=(x+6)2164x29.3x2(2x3)x2(x+10).(2x+3)
" "
=((x+6)^2-4^2)/((2x)^2-3^2).(3x^2(2x-3))/(x^2(x+10)).(2x+3)=(x+6)242(2x)232.3x2(2x3)x2(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)a2b2=(ab)(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+64)(x+6+4)(2x3)(2x+3).3x2(2x3)x2(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)