# Graph (g(x)(3x))/(x^2+3x-54)

g(x)(3x)x2+3x-54
Simplify.
Multiply both sides of the equation by (x-6)(x+9).
3yx2=0⋅((x-6)(x+9))
Simplify 0⋅((x-6)(x+9)).
Expand (x-6)(x+9) using the FOIL Method.
Apply the distributive property.
3yx2=0⋅(x(x+9)-6(x+9))
Apply the distributive property.
3yx2=0⋅(x⋅x+x⋅9-6(x+9))
Apply the distributive property.
3yx2=0⋅(x⋅x+x⋅9-6x-6⋅9)
3yx2=0⋅(x⋅x+x⋅9-6x-6⋅9)
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
3yx2=0⋅(x2+x⋅9-6x-6⋅9)
Move 9 to the left of x.
3yx2=0⋅(x2+9⋅x-6x-6⋅9)
Multiply -6 by 9.
3yx2=0⋅(x2+9x-6x-54)
3yx2=0⋅(x2+9x-6x-54)
Subtract 6x from 9x.
3yx2=0⋅(x2+3x-54)
3yx2=0⋅(x2+3x-54)
Multiply 0 by x2+3x-54.
3yx2=0
3yx2=0
Divide each term by 3×2 and simplify.
Divide each term in 3yx2=0 by 3×2.
3yx23x2=03×2
Simplify 3yx23x2.
Cancel the common factor of 3.
Cancel the common factor.
3yx23x2=03×2
Rewrite the expression.
yx2x2=03×2
yx2x2=03×2
Cancel the common factor of x2.
Cancel the common factor.
yx2x2=03×2
Divide y by 1.
y=03×2
y=03×2
y=03×2
Simplify 03×2.
Cancel the common factor of 0 and 3.
Factor 3 out of 0.
y=3(0)3×2
Cancel the common factors.
Factor 3 out of 3×2.
y=3(0)3(x2)
Cancel the common factor.
y=3⋅03×2
Rewrite the expression.
y=0x2
y=0x2
y=0x2
Divide 0 by x2.
y=0
y=0
y=0
y=0
Find where the expression 0 is undefined.

The vertical asymptotes occur at areas of infinite discontinuity.
No Vertical Asymptotes
3yx2(x-6)(x+9)=0 is an equation of a line, which means there are no horizontal asymptotes.
No Horizontal Asymptotes
Since there is no remainder from the polynomial division, there are no oblique asymptotes.
No Oblique Asymptotes
This is the set of all asymptotes.
No Vertical Asymptotes
No Horizontal Asymptotes
No Oblique Asymptotes
Graph (g(x)(3x))/(x^2+3x-54)