Answer :
Answer:
The simplified given rational expression is [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex].
Step-by-step explanation:
Given rational expression is
[tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}[/tex]
Now to simplify the given rational expression:
[tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}[/tex]
[In the above expression 6 and 3 cancelled and the result is 2, (x-2) and (x-2) getting cancelled each other]
[tex]=\frac{2x(x+3)}{x+9}[/tex]
Now applying distributive property to the above expression
[tex]=\frac{2x^2+6x}{x+9}[/tex]
Therefore [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex]
Therefore the simplified given rational expression is [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex]