Algebraic Fraction

1. Sep 7, 2005

aricho

hey,
I am having trouble with the following...

(6x^2+5x-6)/(6x^2+13x+6) TIMES (3x^2-4x-4)/(3x^2-8x+4)

i can factorise them but i dont know what to do after that...

2. Sep 8, 2005

Fermat

You're meant to simplify the expression, yes?

Just cancel out the common factors. I don't think it can be simplified any further

3. Sep 8, 2005

aricho

yer, but what is left is nasty haha and its wrong

4. Sep 8, 2005

thorney

it simplifys all the way too 1 eventually doesn't it?

5. Sep 8, 2005

aricho

ummm nar.....

this is what i can get to...
{(3x+3)(2x-2)/(2x+3)(3x+2)} + {(3x+2)(x-2)/(3x-2)(x-2)}

{2(9x^2+4)}/(3x-2)(3x+2)

i just dont know how to get there haha

6. Sep 8, 2005

aricho

nice...it does....how about it with a plus instead of a multiply between the two factions

7. Sep 8, 2005

bomba923

Hmm, I seem to get
$$\left( {\frac{{6x^2 + 5x - 6}} {{6x^2 + 13x + 6}}} \right)\left( {\frac{{3x^2 - 4x - 4}} {{3x^2 - 8x + 4}}} \right) = \left[ {\frac{{\left( {3x + 2} \right)\left( {2x - 3} \right)}}{{\left( {3x + 2} \right)\left( {2x + 3} \right)}}} \right]\left[ {\frac{{\left( {3x + 2} \right)\left( {x - 2} \right)}}{{\left( {3x - 2} \right)\left( {x - 2} \right)}}} \right] = \frac{{\left( {3x + 2} \right)\left( {2x - 3} \right)}}{{\left( {3x - 2} \right)\left( {2x + 3} \right)}}$$

Then I suppose?

$$\frac{{6x^2 + 5x - 6}}{{6x^2 + 13x + 6}} + \frac{{3x^2 - 4x - 4}} {{3x^2 - 8x + 4}} = \frac{{\left( {3x + 2} \right)\left( {2x - 3} \right)}}{{\left( {3x + 2} \right)\left( {2x + 3} \right)}} + \frac{{\left( {3x + 2} \right)\left( {x - 2} \right)}}{{\left( {3x - 2} \right)\left( {x - 2} \right)}} = \frac{{\left( {2x - 3} \right)\left( {3x - 2} \right) + \left( {3x + 2} \right)\left( {2x + 3} \right)}}{{\left( {2x + 3} \right)\left( {3x - 2} \right)}} =$$
$$\frac{{2x - 3}}{{2x + 3}} + \frac{{3x + 2}}{{3x - 2}} = \frac{{12\left( {x^2 + 1} \right)}}{{\left( {2x + 3} \right)\left( {3x - 2} \right)}} = \frac{4}{{3x - 2}} - \frac{6}{{2x + 3}} + 2$$

Last edited: Sep 8, 2005
8. Sep 8, 2005

aricho

is that with a plus in between the fractions?

9. Sep 8, 2005

bomba923

Yes, LaTex doesn't clearly space out the signs

10. Sep 8, 2005

TD

I believe it's a but simpler, perhaps you made some slight mistakes.

$$\frac{{6x^2 + 5x - 6}} {{6x^2 + 13x + 6}} \cdot \frac{{3x^2 - 4x - 4}} {{3x^2 - 8x + 4}} = \frac{{\left( {2x + 3} \right)\left( {3x - 2} \right)}} {{\left( {2x + 3} \right)\left( {3x + 2} \right)}} \cdot \frac{{\left( {x - 2} \right)\left( {3x + 2} \right)}} {{\left( {x - 2} \right)\left( {3x - 2} \right)}} = 1$$

Cancels out nicely

11. Sep 8, 2005

aricho

hmmm, maybe the answer is wrong.... it says {2(9x^2+4)}/(3x-2)(3x+2)

12. Sep 8, 2005

thorney

or for the multiplication one you can expand the polynomial and the top clearly equals the bottom with reduced thinking needed!

Last edited: Sep 8, 2005