How do you simplify and find the restrictions for (x^2+3x-18)/(x^2-36)?

3 Answers
Nov 16, 2017

The restricted values of x are: x_1=6 and x_2=-6.

Explanation:

There is no simplification possible.

To find the restrictions you have to see for what values of x there's no solution. That would be when the denominatior is 0.

So you get,
x^2-36=0

you isolate x,
x^2=36

and you do the square root in both sides,
x=+-sqrt(36)=+-6

so these are the restricted values on x:
x_1=6
x_2=-6

Nov 16, 2017

f(x)=(x^2+3x-18)/(x^2-36)=((x-3)(x+6))/((x-6)(x+6))=(x-3)/(x-6)

( f(x)=0<=>x=3

  • x≠6 and x≠-6
    Df=(-oo,-6)U(-6,6)U(6,+oo)
    Df= R-{-6,6} )
Nov 16, 2017

(x^2+3x-18)/(x^2-36) simplifies to (x-3)/(x-6) with the restriction that x!=6 and x!=+6

Explanation:

(x^2+3x-18)/(x^2-36)

color(white)("XXX")=((x+6)(x-3))/((x+6)(x-6))

color(white)("XXX")Note the division is only defined if x!=+-6

color(white)("XXX")=(x-3)/(x-6) provided (x+6)!=0