Algebra 2 Help: Simplifying a Complex Fraction with Step-by-Step Guide

[-1337-]

Well, I need help solving the next problem:

x² + x - 30 over 2x² + 9x -10 multiplied by 4x² - 2x over x² - 36

All you have to do is simplify it. Also, would you be so kind and show your work? Thank you.

 

[topsquark]

Well, I need help solving the next problem:


All you have to do is simplify it. Also, would you be so kind and show your work? Thank you.

$$\frac{x^2+x-10}{2x^2+9x-10} \frac{4x^2-2x}{x^2-36}$$

I would start by factoring each polynomial. You will find there are several cancellations.

If this doesn't seem that informative, remember that YOU need to show your work so we can find where you need the help!

-Dan

 

[-1337-]

$$\frac{x^2+x-10}{2x^2+9x-10} \frac{4x^2-2x}{x^2-36}$$

I would start by factoring each polynomial. You will find there are several cancellations.

If this doesn't seem that informative, remember that YOU need to show your work so we can find where you need the help!

-Dan

It's impossible to factor "2x² + 9x -10" isn't it?

 

[d_leet]

$$\frac{x^2+x-10}{2x^2+9x-10} \frac{4x^2-2x}{x^2-36}$$

I would start by factoring each polynomial. You will find there are several cancellations.

If this doesn't seem that informative, remember that YOU need to show your work so we can find where you need the help!

-Dan

Have you tried to factor any of those? The only 2 that factor don't cancel out.

 

[topsquark]

Have you tried to factor any of those? The only 2 that factor don't cancel out.

Crap! I factored the 2x^2+9x-10 wrong. You are correct. There is either a typo in the original or the problem is bad. (Or someone made the same mistake I did!)

-Dan

 

[d_leet]

I can factor all but the $$x^2+x-10$$. Usually more cancels out in these problems though.

Take a look at $$2x^2+9x-10$$. Since 2 is prime this will factor somehow into a product that looks like $$2x^2+9x-10=(2x+a)(x+b)=2x^2+(a+2b)x+ab$$. a and b are factors of 10. What might they be?

-Dan

That doesn't factor into integers if you create a system of equations you end up back where you started, and if you try the quadratic equation you don't get rational numbers.

 

[-1337-]

I'm terribly sorry, it's x² + x - 30, not x² + x -10, but I can factor that. Also, can you explain, please, I have to go to bed soon.

 

[d_leet]

I'm terribly sorry, it's x² + x - 30, not x² + x -10, but I can factor that. Also, can you explain, please, I have to go to bed soon.

Well then some more things cancel out, are you sure that it was 2x^2+9x-10 in the original problem because if that's wrong then more things may cancel.

 

[-1337-]

Well then some more things cancel out, are you sure that it was 2x^2+9x-10 in the original problem because if that's wrong then more things may cancel.

Yes, I'm positive about the 2x² + 9x -10. I guess my teacher didn't write the problem correctly.

I know how to factor the x² + x - 30 and the x² - 36, but not the other two.

 

[topsquark]

I'm terribly sorry, it's x² + x - 30, not x² + x -10, but I can factor that. Also, can you explain, please, I have to go to bed soon.

That helps. Please note the correction I made to my last post. I screwed up and didn't notice before I posted.

I can factor the new polynomial, but still nothing cancels. Are you certain about the 2x^2+9x-10?

-Dan

 

[d_leet]

Yes, I'm positive about the 2x² + 9x -10. I guess my teacher didn't write the problem correctly.

Ok well, with the other correction there are some things which cancel if you factor every polynomial so do you think you can give it a try now?

 

[d_leet]

That helps. Please note the correction I made to my last post. I screwed up and didn't notice before I posted.

I can factor the new polynomial, but still nothing cancels. Are you certain about the 2x^2+9x-10?

-Dan

One thing will cancel. There is a common factor between x^2+x-30 and x^2 - 36.

 

[-1337-]

Thank you for all of your help. I'll ask my teacher tommorow.

Also, something does cancel out. If you factor x² + x - 30 you get (x + 6)(x - 5), and if you factor x² - 36 you get (x + 6)(x - 6). The (x + 6)' s cancel each other other out.

 

[topsquark]

One thing will cancel. There is a common factor between 2x^2+9x-10 and x^2 - 36.

As you pointed out, 2x^2+9x-10 doesn't factor.

-Dan

 

[d_leet]

As you pointed out, 2x^2+9x-10 doesn't factor.

-Dan

Whoops I pasted the wrong thing, I fixed my post, sorry about that.

 

[ksinclair13]

I got this as my answer:

$$\frac{2x(x-5)(2x-1)}{(x-6)(2x^2+9x-10)}$$