Expert: Richard J. Raridon - 5/23/2010

Question
QUESTION: im confused on this problem. im supposed to solve the equation and then identify it as an identity or contradiction if possible.  i dont think its either one. i got z=-2, but a calculator tells me that there is no solution.
2z+3   3z-4   z-2
____ + ____ = ___
3       6     2

ANSWER: It's a lot clearer if you write it (2z+3)/3 +(3z-4)/6 = (z-2)/2
z = -2 is the correct answer, which you can certainly show by putting in that solution and find that both sides are -2.    Either you didn't enter it into your calculator correctly or you need to buy a new calculator.  

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QUESTION: |-1-2x|>5 my answer= x<-3 or x>2
|1/2x-3|-4<2 my answer = x>-6 or x<18

i cant seem to figure this one out: 3|1/3(x-2)|+2<or=to3 need help

ANSWER: Your answers are correct. For 3|1/3)(x-2)|+2 <= 3, 1 <= x <= 3

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QUESTION: x/x^2-16 - x/x+4 + 4/x.  i cant seem to figure this out.  i factored out the x^2-16 with (x+4)(x-4) and from here i got confused. what am i doing wrong?

complex fraction = 1/c + 1/d / c/d - d/c = my answer d+c/cd.  

complex fraction = x-y/x^-1 - y^-1 = i got stuck on this.  i changed the negative x and y denominators to 1/x and 1/y then tried to multiply xy by top and bottom.im not certain that its right so i just stopped.

-w^3 - 216 another question im stuck on.  do you factor the cubed formula (w+6) (w^2-2w+4)= i dont think this can be done this way.

thanks again for all your help

Answer
To avoid confusion you should write it x/(x^2-16) -x/(x+4) +4/x
so your LCD is x(x^2-4) giving you x^2/x(x^2-16) -x^2(x-4)/x(x^2-16) +4(x^2-16)/x(x^2-16)
= (-x^3+9x^2-64)/[x(x^2-16)]
(1/c+1/d)/(c/d-d/c) = [(c+d)/(cd)][(cd)/(c^2-d^2)] = 1/(c-d)
(x-y)/(1/x-1/y) = (x-y)(xy)/(y-x) = -xy
If you had multiplied (w+6)(w^2-2w+4) you would have realized you didn't factor correctly
-(w^3+216) = -(w+6)(w^2-6w+36)