Algebra help

[dchipman]

I have been out of math for quite a while. I have an economics class that i am taking in the fall for my MBA. My instructor sent some sample problems he felt we should be able to do. I am stuck.

Also, there is an equation that i have tried to remember but it to is alluding me.
its starts like this:

-b +/- sq rt of 4ac.... but that is all i can remember.

Here are some problems:
y = ((3x^2 - 3x -15)/(2X^2 -4x-7))/((2x^2 +4x + 5)/(4x^2 +4x-^) solve for x at y=3.0

((ax^(n+1)- bx+c)/(dx^n +ex- f)) = ((gx^n- hx +j)/(kx^(n+1) +px+m)
rearrage and simplify

y = 3x^2 + 6x -7 solve for x at y=0

thanks for the help
daunielle[/u]

 

[Gene]

What you are trying for is the quadratic formula for solving ax^2+bx+c = 0.
x = (-b+sqrt(b^2-4ac))/2a
(+ is plus or minus)
first one:
(4x^2 +4x-^) :?:

They sure are giving you messy equations.
((ax^(n+1)- bx+c)/(dx^n +ex- f)) = ((gx^n- hx +j)/(kx^(n+1) +px+m)
Get rid of the denominators by multiplying by them.
(ax^(n+1)- bx+c)*(kx^(n+1) +px+m) = (gx^n- hx +j)*(dx^n +ex- f)
Expand
a*k*x^(2(n+1))+apx^(n+2)+amx^(n+1)-bkx^(n+1)-bpx^2-bmx+ckx^(n+1)+cpx+cm =
gdx^(2n)+gex^(n+1)-gfx^n-hdx^(n+1)-hex^2-hfx+jdx^n+jex-jh
(whew!)
Gather the multipliers of the same powers of x on the left side such as
(am-bx+ck-ge+hd)x^(n+1)
in descending order of exponents.

The last one you can use the formula on.

 

[dchipman]

Thanks again for your help Gene.
For this equation

y = ((3x^2 - 3x -15)/(2X^2 -4x-7))/((2x^2 +4x + 5)/(4x^2 +4x-^) solve for x at y=3.0

do i first multiply by the deminators then solve for y?
Division of quadratic formulas is quite irritating.
Thanks
daunielle

 

[Gene]

First you fix up 4x-^)
Then you bring the denominator to the top with (a/b)/(c/d) = ad/(bc) then set y=3 to get
3(bc)=ad
multiply every thing out, gather terms on the left and see how it looks. I would have expected some things to have canceled out at the ad/(bc) point but can't tell yet. Nothing I see factors "neatly" which is almost standard practice in this type of problem.