How do you simplify #(x^3 - 9x) / (x^2 - 7x + 12)#?

2 Answers
May 21, 2018

Answer:

#(x(x+3))/(x-4)#

Explanation:

#"factorise numerator and denominator"#

#color(magenta)"factor numerator"#

#"take out a "color(blue)"common factor "x#

#=x(x^2-9)#

#x^2-9" is a "color(blue)"difference of squares"#

#"which factors in general as"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#"here "a=x" and "b=3#

#rArrx^2-9=(x-3)(x+3)#

#rArrx^3-9x=x(x-3)(x+3)larrcolor(red)"factorised form"#

#color(magenta)"factor denominator"#

#"the factors of + 12 which sum to - 7 are - 3 and - 4"#

#rArrx^2-7x+12=(x-3)(x-4)larrcolor(red)"factored form"#

#rArr(x^3-9x)/(x^2-7x+12)#

#=(x(x-3)(x+3))/((x-3)(x-4))#

#"cancel the "color(blue)"common factor "(x-3)#

#=(xcancel((x-3))(x+3))/(cancel((x-3))(x-4))=(x(x+3))/(x-4)#

#"with restriction "x!=4#

May 21, 2018

Answer:

#(x(x+3))/(x-4#

Explanation:

#(x^3-9x)/(x^2-7x+12)#
#color(teal)(=(x(x^2-9))/(x^2-3x-4x+12)#

#color(blue)(=(x(x+3)(x-3))/((x-3)(x-4))#

#color(magenta)(=(x(x+3)cancel((x-3)))/(cancel((x-3))(x-4))#

#color(green)(=(x(x+3))/(x-4#

Ans that's your answer.

P.S.: Isn't the solution #color(blue)c#olorful?