How do you simplify (x^3 - 9x) / (x^2 - 7x + 12)?
2 Answers
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
Explanation:
Ans that's your answer.
P.S.: Isn't the solution
