I'm in Calculus and I forgot how to solve this algebraically. I know who to do this graphically, but the problem's asking to solve this without graphing. Sorry if I sound dumb.\n\nlim((x-1+(x+1)^(-1))/x) as x approaches 0
127094
the clue would be to simplify the equation  to \nlim {x +[-(x+1)+1]}/(x+1)\n x-->0 \nlim [x + 1 -x]/(x+1)\nx-->\nlim (1/(x+1)) =1\nx-->0
349464
Use the quadratic formula.\nx1 = 1\nx2 = -1/2
362291
you basically have to factor the whole problem out, i.e:\n\nthe given equation factors out to:\n\n(x-4)(x+4)\n\nSo the domain is all real numbers except 4 and -4. This is so, because when x is either 4 or -4 the equation is equal to zero.
427129
The issue lies in the fact that the original equation is 0=0.\n\nThen, if you put in any value for x, you are dividing by 0 which as we all know, is a "no no."
388563
Just split it into parts - when is x-x^2<0, and when is it >0?\nThat bit has roots 0 and 1, so it is positive between 0 and 1, negative everywhere else.\n\nThus, ∫(x=-1 to x=0) (x^2-x) dx + ∫(x=0 to x=1) (x-x^2) dx + ∫(x=1 to x=3) (x^2 - x) dx\n\n= [(1/3 x^3 - 1/2 x^2) from -1 to 0] + [(1/2 x^2 - 1/3 x^3) from 0 to 1] + [(1/3 x^3 - 1/2 x^2) from 1 to 3]\n= (0- -5/6) + (1/6 - 0) + (9/2 - -1/6)\n= 17/3.
298240
Joel, you need some help.  This is one of the easiest questions I have ever heard!  You should know this, man!  You're gonna fail your test if you keep cheating on here and don't actually figure out how it works.  Good luck, brotha'\n\nL = -2 or L(x) = -2
182467
While Albert has found the correct solution using calculus, the question asked how to find the solution with graphing.  So, if you don't care how you find the answer, use Albert's.  But if you need to graph it to find the solution, you use the function that Albert got V(x)=x(6-2x)(8-2x) and graph the resulting cubic function (explained well by Just Wondering).  You will see a graph that increases from -infinity up to about 24 (on the V), then decreases to about -3.5, and then increases to infinity.  You want to find the x value and V value at that first "hump," or maximum.  If you are using a graphing calculator you can use the "Maximum" function to see that Albert's answer is approximately correct.
455314
if it x - 4x/(x+1) = 4/(x+1)\nthen x(x+1) - 4x = 4\nor x^2-3x + 4 = 0\n\nthis is quadratic and so 2 solutions so Megan is right\n\nyou do not have tro evaluate
337557
( x^2 -x +2 )( x^2 + x + 2 )\n\n=>\n a= -1\n b= +2\n c= +1\n d= +2
212680
When you say "x2", I assume you mean "x^2" - that's how you say x-squared.\n\nYou have to factor, so use reverse FOIL. Set up:\n\n(__ +/- __) (__ +/- __)\n\nYou know what needs to go in the first blank in each parenth to get x^2 (don't you?), so start there, then addends for -14, then see what happens when you square those addends.\n\nYou can do this.
494268
let u = x^2 + 1, then you have du = 2xdx, => dx = 1/2x du,\n\nsubstitute back you are on the way  to solve it
309103
Wonderful.\nTHis is some sort of simultaneous equation.\nAccording to the principle of this equation, we try to rationalize one term of the equation so as to get one unknown term. We can either try finding the x term or the y term. For your question as to find the y term.\n\nFirstly, we rationalize the x terms by multipling them by the inverts. then it will result to \n                                    12x + 20y = 32\n                                    12x + 18y = 39\nThe we apply the subtraction rule. ie. we multiply all the terms beneath by the negative (-) sign. This will result to \n                                    12x + 20y = 32\n                                   -12x - 18 = -39\nWe later subtract so as to attain\n                                2y = -7\nWe apply the law of linear equation by dividing both sides by the coefficient which in this case is 2.\n                              2y/2 = -7/2\nThis will eventually cancel the 2 in the first term therby leavin y alone. \n The answer will be in either of the following cases through simplification.  -7/2, -3 1/2 or -3.5
465034
I think there is a sign error: the cubic term is supposed to be -2x^3, not 2x^3. Then the other roots are 3 and -1 and the factors are\n\n(x-8i)(x+8i)(x-3)(x+1)
14593
(x-2)/(x^2-2x-15)+(x+2)/(5-x)\n(x-2)/((x+3)(x-5))+(x+2)/(5-x)\n(x-2)/((x+3)(x-5))+(-2-x)(x+3)/(x-5)(x+3)\n\n[(x-2) + (x+3)(-2-x)] / [(x+3)(x-5)]\n\nANSWER :\n(x^2+4x+8)/((x+3)(5-x))
135967
*(2x/(x^2-4)) + (5/2-x) - (1/2+x)\n*(2x/(x^2-4)) + (5/2-x)((2+x)/(2+x)) - (1/2+x)((2-x)/(2-x))\n*(2x/(x^2-4)) + (10+5x)/(4-x^2) - (2-x)/(4-x^2)\n*(2x/(x^2-4)) + (8+6x)/(4-x^2)\n\nyou should be able to get it from there
437273
I already answered this in the other thread. Theres no solution: |2x-1| >= 0, so the left hand side is >= 0 + 3 = 3.\nNote that I'm not telling you that you did something wrong - 'no solution' is a perfectly legal answer to 'solve for x'.
376210
C is correct but not complete... only the 3 is factored out... the real answer would be:\n\n3(x-1)(x+4)