simplyifying expression

[Rani]

3x^2-18x/-9x^2
3x(x-6)/-3x(3x)=x-6/-3x
Is it correct.

 

[Deleted member 4993]

(3x^2-18x)/(-9x^2)

(3x(x-6))/(-3x(3x)) = (x-6)/(-3x) = (6-x)/(3x) = 2/x - 1/3

Is it correct.

Those parentheses are VERY important.

 

[mmm4444bot]

(x-6)/(-3x)

Is it correct[?]

Yes, but Subhotosh's form (where he factors out -1 from both numerator and denominator and then cancels them) is better.

(6 - x)/(3x)

I would leave it at this.

As an aside, do you know? A negation sign in a ratio can float at will from numerator to denominator to out-in-front of the ratio, wherever it is convenient to place it.

\(\displaystyle \frac{x - 6}{-3x} = -\frac{x - 6}{3x} = \frac{-(x - 6)}{3x}\)

 

[Rani]

In the back of book the answer is (6-x)/3x

 

[mmm4444bot]

In the back of book the answer is (6-x)/3x

That's same as Mark's

(6 - x)/3x does not look the same as Subhotosh's or Mark's answer, to me.

Try squinting your eyes, Denis.