Simplifying Rational Expressions

[malelia123]

Hey Guys,
I AM SO STUCK!!!

Here is the rational Expression to be simplified

10x^2 - 8x / 24x-30x

I've worked this out with everything I can possibly think of 2x/2x then dividing by 3
but the answer in the text is
1/3 (With a negative can't exactly remember I forgot my textbook at home)

PLEASE help, show me the steps and tell me how the heck to do this!

Thank you!

 

[JeffM]

Hey Guys,
I AM SO STUCK!!!

Here is the rational Expression to be simplified

10x^2 - 8x / 24x-30x

I've worked this out with everything I can possibly think of 2x/2x then dividing by 3
but the answer in the text is
1/3 (With a negative can't exactly remember I forgot my textbook at home)

PLEASE help, show me the steps and tell me how the heck to do this!

Thank you!

Factoring out and then cancelling 2x is a good first step

\(\displaystyle \dfrac{10x^2 - 8x}{24x - 30x} = \dfrac{2x(5x - 4)}{2x(12 - 15)} = \dfrac{5x - 4}{12 - 15} = - \dfrac{5x - 4}{3} \ne - \dfrac{1}{3}.\)

I suspect however the problem was

\(\displaystyle \dfrac{10x^2 - 8x}{24x - 30x^2} = \dfrac{2x(5x - 4)}{2x(12 - 15x)} = \dfrac{5x - 4}{12 - 15x} = \dfrac{5x - 4}{-(3)(5x - 4)} = - \dfrac{1}{3}.\)

It always helps to write the problem down correctly.

 

[DrPhil]

Hey Guys,
I AM SO STUCK!!!

Here is the rational Expression to be simplified

(10x^2 - 8x) / (24x - 30x^2)

I've worked this out with everything I can possibly think of 2x/2x then dividing by 3
but the answer in the text is
1/3 (With a negative can't exactly remember I forgot my textbook at home)

PLEASE help, show me the steps and tell me how the heck to do this!

Thank you!

Please use extra parentheses when writing rational expressions inline, so that the order of operations is clear.

I'm GUESSING that one of the two terms in the denominator is x^2. If it is the second term, then the answer will be what you want.

2x/2x is a very good start: factor 2x out of top and bottom, then cancel:

\(\displaystyle \dfrac{10x^2 - 8x}{24x - 30x^2} = \dfrac{2x(5x - 4)}{2x(12 - 15x)} = \dfrac{5x - 4}{(-3)(5x - 4)} = \cdots \)

In other words, I think you were doing everything right except for getting the question copied!

 

[malelia123]

Thanks!

Seriously thought I was going crazy, I even tried to sleep on it because I figured I was missing something Very simply!!
Thank you so much.
you are life savers!!