babybear said:
I am so lost on this.
Please help. How do I Multipy and Simplify this problem?
I need step by step instructions.
3x-6 . 2x^2-3x+1
x-1 . x^2-x-2
(3x-6) /(x-1) * (2x^2 -3x +1) / (x^2 -x -2)
The left fraction factors on the top:
3(x-2)/(x-1) As for the right fraction . . . Now we get into some more involved factoring. . .
Factoring a trinomial is a process of un-FOILing -->
(2x^2 -3x +1) The 1st term is the result of multiplying the Firsts, so we start with: (2x )(x )
The 3rd term is the result of multiplying the Lasts. Since the 3rd term is +, we know the signs inside the ( ) are the same. Since the middle term is -, we know that both signs are neg -->
(2x - )(x - ) The only factors of 1 are 1 * 1, so put those in for the Lasts and then FOIL to be sure it works.
(2x - 1 )(x - 1 )
And then the denominator on the right . . .
(x^2 -x -2)
(x )(x ) 3rd term is neg, so signs are different -->
(x + )(x - ) Factors of 2 are 2*1 The negative sign in the middle term tells us that the larger factor goes with the neg sign -->
(x + 1 )(x - 2 ) Again, FOIL it quickly just to be sure it's correct.
All together, we have:
[3(x-2) / (x-1)] * [(2x - 1 )(x - 1 ) / (x + 1 )(x - 2 )]
Now cancel any factors that are the same top and bottom.
The (x-1)'s will cancel as well as the (x-2)'s.
What's left on the top and bottom?
3 * (2x-1) / (x+1) Just multiply the 3 by EACH value inside the ( ) on top.
