Simplify this algebraic expression

[Gringo123]

How can I simplify this expression? As it is already factorised (factored) I do not see what else I can do to simplify it.

x(9x+2) / x³(x-2)

The only thing that I can think of is if I unfactorise everything to give the following:(although it doesn't seem to be very simplified from the original expression)

x² + 2x / x⁴ - 2x³

which gives... 2x / x² - 2x³

 

[HallsofIvy]

General rule- never "unfactorize" unless you see very good reason to!

Here, you should be able to see the "x" factor in the numerator and "$x^3$" in the denominator and immediately cancel. What's left, 9x+2 and x- 2, have no common factor so the simplest form is $(9x+2)^2/(x-2)$

In what you wrote, you seem to have forgotten the "9" in the numerator.

Also, you cannot cancel, in numerator and denominator, things that are added. $(x^2+ 2x)/(x^4- 2x^3)$ is NOT $2x/(x^2- 2x^3)$.

 

[Gringo123]

Thanks a lot Hall of Ivy!

 

[Mark44]

How can I simplify this expression? As it is already factorised (factored) I do not see what else I can do to simplify it.

x(9x+2) / x³(x-2)

The only thing that I can think of is if I unfactorise everything to give the following:(although it doesn't seem to be very simplified from the original expression)

x² + 2x / x⁴ - 2x³

which gives... 2x / x² - 2x³

Whenever there are two or more terms in the numerator or denominator, parentheses are needed around the numerator or denominator, or both.

More seriously, you are cancelling terms in the numerator or denominator that are not factors. By this same logic we would say that (1 + 2)/(2 + 7) = 1/7, which is clearly incorrect.