The simplified form of the given expression has a numerator (x + 9)(2x + 1) and the denominator (x + 7) and the expression does exist at (x = 9) and this can be determined by factorizing the given expression.
Given :
Expression --- [tex]\dfrac{3x^2 -27x}{2x^2+13x-7}\div \dfrac{3x}{4x^2-1}[/tex]
First, factorize the expression [tex]4x^2-1[/tex].
[tex]4x^2-1=(2x-1)(2x+1)[/tex]
Now, factorize the equation [tex]2x^2+13x-7[/tex].
[tex]2x^2+13x-7 = 2x^2+14x-x-7[/tex]
[tex]=2x(x+7)-1(x+7)[/tex]
[tex]=(2x-1)(x+7)[/tex]
Now, factorize the equation [tex]3x^2-27x[/tex].
[tex]3x^2-27x=3x(x-9)[/tex]
Now, substitute the factorized terms in the given expression.
[tex]\dfrac{3x(x-9)}{(2x-1)(x+7)}\div \dfrac{3x}{(2x-1)(2x+1)}[/tex]
Simplify the above expression.
[tex]=\dfrac{(x+9)(2x+1)}{(x+7)}[/tex]
For more information, refer to the link given below:
https://brainly.com/question/25834626
