algebra- adding fractions with variables?
455994
The answer is X = -2\n\nYou were right the first time.  You just made a calculation mistake when you tried to check it.\n\nHere's the check I got (I entered periods as spacers):\n\n_1_...+..._2_....=....0\n2+3x......2-3x  \n\n___1__...+...___2__....=....0\n2+3(-2).........2-3(-2)\n\n_1_...+..._2_....=....0\n2-6........2+6\n\n_1_...+..._2_...=...0\n-4...........+8\n\n_1_...+.._1_...=...0\n-4..........+4\n\n0...=...0\n\nTo get to the x = -2, we do what you did with (2 + 3x)(2 - 3x) as the common denominator.  When we multiply it out (multipying the common denominator to both sides of the equation), we get:\n\n2 -3x + 4 + 6x = 0\n6 + 3x = 0\n3x = -6\nx = -2\n\nYou asked a question above about the result of multiplying the common denominator to the right half of the equation.  Of course, multiplying anything times "0" always equals "0".  Right?\n\nGood luck!
913289
You end up with a remainder, so it's not pretty, but you should be able to do long division and get:\n\n3x^2 - 4x + (16/3) - 23/(3*(3x+2))
1034542
The steps for adding two fractions:\n\n1) reduce both fractions  (not strictly necessary, as long as you reduce in the end)\n2) give them both the same demoninator (the bottom number)\n3) add the top numbers (the numerators)\n4) reduce the answer\n\nSo, step one is already done.\n\nStep two is to give them a common (the same) denominator.  So what number should that be?\n\nIt's going to be the product of both denominators.  so 3 * 8 = 24.  So that's our common denominator.\n\nWhat you are going to do is to multiply the top and bottom half of each fraction by the same number (which is okay, it's equivilant to multiplying by 1) so that the bottom number is 24.  So for the left fraction, we will multiply the top and bottom by 3.  So we get (3 *3)/(8 * 3), which is 9/24.\n\nAnd now we multiply the second fraction, top and bottom, by 8.  so (2 * 8)/(3 * 8) = 16/24.  Now that both fractions have the same denominator, we add them by adding the top numbers, and putting that over the common denominator.  So 9 + 16 = 25, so we get 25/24.\n\nThis is technically acceptable, but teachers will probably want you write this as 1 and 1/24th.
707566
If the value of the new fraction is 1/2, that means the denominator is 2 times the numerator. Let's say, then, that the value of the original numerator is x, the value of the original denominator as y.\n\nThen\n(3+x)/(1+y) = 1/2\n\nmultiply both sides by (1+y)\n\n(3+x)=(1+y)/2\n\nmultiply both sides by 2\n\n2(3+x) = (1+y)\n\nSince we want the original fraction, we want x/y\n\n6+ 2x = 1+y \n\ny = 5 + 2x\n\nsubstituting 5+ 2x for y\n\nx/(5+2x)\n\nInsert any non-zero integer into the above, to get your original fraction. For example, if x=1, then the fraction is 1/7. To check to see if that's correct, let's add 3 to the numerator and 1 to the denominator. We then get 4/8, which is equal to 1/2!\n\nYou could also guess and check this. Start by taking fractions equal to 1/2. Let's start with the smallest after 1/2, which is 2/4. Subtract 3 from the numerator, and 1 from the denominator. Well, we get a negative numerator, so let's skip this one. Okay, then 3/6. Subtracting 3 from the numerator gives 0, which makes the original "fraction" 0, which doesn't work. 4/8: 4-3 = 1 and 8-1 = 7. That means our original fraction could be 1/7, and we've found an answer. Hope this helps!
696212
find the common denominator\nmultipy the top and bottom of the fraction so the denominators are equal and then add the numerator
555590
Just multiply:\n(X/3)(3/4 x) -(x/3)(3/5) + (3/4)(3/4x) - (3/4)(3/5)\n\nand simplify from there
282749
You will need to place the parentheses at the proper places. To help you out, I have assumed where they will be and solved it. Please confirm if these are correct. If not, rewrite the problem and I will try to solve it.\n\nThe text you find in between the steps is an explantion of what I have done...\n\n(7x/(x^2 + 4x)) divided by (35x^2/ x+4). This is my assumption.\n\nRewriting the problem in mathematical form\n= (7x/(x^2 + 4x))/(35x^2/ x+4)\n\n\nDividing by a fraction is the same as multiplying by its reciprocal\n= (7x/(x^2+4x)))*((x+4)/35x^2)\n\nRewriting after moving out the dommon factor in the denominator of the first fraction. [x^2+4x = x(x+4)]\n= (7x/(x(x+4)))/35x^2/(x+4) .)\n\nCanceling out the common terms in the numerator and denominator. Here it is (x+4)\n= (7x/x)*(1/(35x^2))\n\nCanceling out more terms. Here it is x\n= 7/(35x^2)\n\nCanceling out more terms. Here the number 7\n= 1/5x^2\n\nThis will be the final answer.
889005
Those are mixed numbers.  They consist of a whole number plus a fraction.  To add them you need to convert both mixed numbers to what's called 'improper' fractions, convert those fractions to have the same denominator, and then add the numerators.  You usually convert the result back to a mixed number.\n\nSo, what is 3 1/2?  This is really 3+1/2.  Change the 3 to a fraction:\n\n3+1/2 = 3/1+1/2=6/2+1/2=7/2\n\nNow, do the same with the other number:\n4+1/2=8/2+1/2=9/2\n\nNow add:\n7/2+9/2 = (7+9)/2= 16/2 = 8.\n\nThat's it.  \n\nAlso, think about adding just the whole numbers:\n3+4=7\nand just the fractions:\n1/2+1/2 =1\n\nNow, add those:\n\n7+1=8.
926120
your variable is x so you replace that with 8, since x=8     since there are no signs between the 9 and x  in  9x  , that means to multiply them  so that is 72       so your answer is 72 + 5 or 77  , hope that helps
965349
I believe you meant (2x^2 - 3x - 2 )/ (10 + x - 3x^2) right?\n\nWell we can rearrange the problem to look like (2x^2 - 3x - 2 )/ (- 3x^2+ x +10)\n\nWe now factor out the top and factor out the bottom.\n[(2x +1) (x-2)] / [(-3x-5)(x-2)]\n\nSince this is a fraction, we can cancel out the (x-2) because it is on top and the bottom.\n\nWe are left with:\n(2x +1) / (-3x-5)\n\nI think this is what you wanted, good luck and be careful of how you write your notation!
223041
uh..... no. Unless I am missing something, you substitute the 3 for 'x' and the 2 for 'y' and get 3+(3 x 2) = 3 + 6 = 9
1109416
3/x  + 1    the way you put it..
965696
Two add two fractions, the denominators must be equal.\n\nThe first step is to convert the addend that is a mixed number (an integer plus a proper fraction) into an improper fraction. Do this by multiplying the integer part by the denominator and then add the numerator of the fraction.\n\nExpress the result as an improper fraction (fraction with value greater than 1) whose numerator is the sum you just calculated and whose denominator is the same as the denominator of the fraction part of the mixed number.\n\nFor example: 2/3 + 4 2/5 = 2/3 + 22/5\n\nNext, find the least common denominator of these two fractions, the smallest integer that contains both denominators as factors. For the example above, this is 15. Multiple both terms by (3*5)/15, which equals 1, and therefore does not change the value of the fraction:\n\n(2/3) * (3*5)/(15) = 10/15 (the 3's "cancel out" since 3/3 = 1)\n(22/5) * (3*5)/(15) = 66/15 (the 5's "cancel out" since 5/5 = 1)\n\nNow add 10/15 + 66/15 by adding the numerators and keeping the same denominator: 76/15.\n\nFinally, express this improper fraction as a mixed number by dividing: 5 1/15
982146
Just add and substract terms in both sides.\n\nSince \ny-x^2+8x\nis equal to 7, \nyou can add x^2 and substract 8x to both sides.\n(y-x^2+8x) +x^2-8x = y\n7 +x^2-8x = x^2-8x+7\n\nso y=x^2-8x+7\n\nby the way, if you factorize in terms of x then you'd get\ny=(x-1)(x-7)
677314
To do this, you do (2/3) / (1/5). You must flip the denomiator fraction over and change the operation to multiplication. So... that would be (2/3) * (5/1) which would be 10/3.
869887
If you have 2 equations, just solve for one variable for one of the equations. Take that equation and plug it into the same variable for the other equation. You will solve for that variable, and plug in that number to any of the 2 equations to solve for the other variable.
323622
You divide fractions by multiplying the reciprical... for example:\n\n1/2 x 8/3 = 8/6 or 4/3\n\nYou simply multiple the numerators together and the denominators together after that