Solve rational equation by using the LCD?
479288
multiply both sides by 12x (that's the LCD)\n12x^2-12+28x^2=27x^2\n13x^2=12\nx=+-sqrt(12/13)\n^2 is squared\n+- is plus or minus, i.e. there are two solutions.
1034089
c = 3/2, b = 1/2.\nBasically, you need to find\n2 = c^2 - b^2 in the rationals.  But, since finding rational solutions is annoying, it's easier finding integer solutions to the equation\n2a^2 = c^2 - b^2\n2a^2 = (c-b)(c+b)\nSince c+b and c-b have the same parity, they need to both be even.  This means that one of them is divisble by 4.  So we need to have a = 2k for some k.\nSo we actually have to solve 8k^2 = (c-b)(c+b), but 8 factors as 4 * 2, so let c+b = 4, c-b = 2, which gives c = 3, b = 1.  But you actually want c/a, b/a, and a = 2, so c= 3/2, b = 1/2 works.\nFor 5, we can just take c = 3, b = 2, and we have that 5 = 9 - 4.
736379
for this just substitute for x and y in eqn and see if LHS=RHS\nLHS=4\nRHS=(-1/2)(-3)-5/2\n=3/2-5/2\n=-2/2\n=-1\nnot = RHS\nso pt. not on line
754366
You need to use the quadratic equation as it is not factorable into rational expressions.\nThe form of the equation is:\nax^2 + bx + c = 0 \nSo in your case,\na = -2, b = 6, c = -3\nand the solution is:\nx = [ -b ± √(b^2 - 4ac) ] / (2a)\n\nso substitute and reduce.\n\nx = [ -6 ± √(6^2 - 4(-2)(-3)) ] / (2(-2))\n\nx = [ -6 ± √(36 - 24) ] / (-4)\n\n= [ -6 ± √12 ] / (-4)\n= [ -6 ± 2√3 ] / (-4) \n= (3 ± √3)/2
857762
Not sure if it's the shortest or nicest way, but I was able to get to a solution using substitution u=x^2, and v=y^2, then adding 1/4 to the v side to make it a quadratic equation, solving for v, then re-substituting, and solving for y.\n\nI got y = sqrt ( sqrt (x^2-x^4+1/4) + 1/2 )\n\nYou should be able to plot that ...
713860
1.Xc=1/2pifc\nc=1/2pifXc\n\n2.ib=ibq+rt(2is)\nib(1-q)=rt(2is)\nsquaring\n[ib(1-q)]^2=2is\ns=[ib(1-q)]^2/2i\n\n3.Q=Xl/R\nXl=Q/R\n\n4.Lt=L1+L2+2Lm\n2Lm=Lt-L1-L2\nLm=[Lt-L1-L2]/2\n\n5.Es=E1+E2+E3\nE2=[Es-E1-E3]\n\n6.R1=i2R^2/i2\ni2R^2=i2R1/i2\nR=rt[i2R1/i2]\n\n7.R1/Rx=R2/R3\nRx=R1R3/R2\n\n8.y=mx+b\nb=y-mx\n\n9.i2=i1R1/i1
858168
1. 14x^2 +21x\n\na good way to start would be to factor out any common terms:\n\n7(2x^2 + 3x)\n\n7x(2x + 3)
259003
Use the quadratic formula.  It works everytime!\nx = (-b plus or minus sprt(b^2 - 4ac))/2\nwhere\nax^2 + bx + c = 0\nSome of these will factor, however not all of them will.
758639
x^2-25x=50\nx^2-25x+625/4=50+625/4\n(x-25/2)^2=(200+825)/4(taking LCD and adding)\nx-25/2=+/-rt1025\nx=25/2+/-rt1025\n=25/2+/-5rt41
438560
__5 _ , x____\n9 – x2 6x+ 18\nI'll take a shot at what I think you are asking.  Is it write each of these two fractions: 5 over 9 minus x squared, and x over 6x + 18?\n\nIf so, factor each denominator: (I'll use x^2 for x squared)\n9-x^2 = (3+x)(3-x)\n6x+18 = 6(x+3)\n\nNote: x+3 = 3+x, so...\n\nThey share a factor of (x+3) so the LCD is 6(x+3)(3-x)\n\nFirst fraction missing 6, so multiply top & bottom by 6\nSecond is missing (3-x) so multiply top & bottom by (3-x)\n\nFirst: 30 over (6(x+3)(3-x))\nSecond: (3x-x^2) over (6(x+3)(3-x))
796617
5/(c + 2)  - 5/(c^2 - 4) = 0\n\nHopefully this is the equation of your problem.\n\nc^2 - 4 is a difference of two squares and factors into (c + 2)(c - 2)\n\nThe LCD of the fractions is (c + 2)(c - 2), and we can clear the fractions by multiplying both sides of the equation by the LCD.\n\n5(c - 2)  - 5 = 0\n5c - 10 - 5 = 0\n5c = 15\nc = 3\n\nCheck\n5/(c + 2)  - 5/(c^2 - 4) = 0\n5/(3 + 2) - 5/(9 - 4) = 0\n5/5 - 5/5 = 0\n0 = 0
127942
hey the eq says 2x> x/2 + 45\nso get x/2+45's lcd\nso that's 2. x+90/2\nso 2x>x+90 all over 2\nthen cross multiply 2\nso it 'll become 4x> x + 90\ntranspose x\nthen 3x>90 didvide both sides by 3 so\nx> 30 that is the answer
812066
Find the lowest common denominator (LCD).\n\ni.e.  1/2 + 1/3\n\nLCD = 2*3 = 6\n\n(1*3)/(2*3) + (1*2)/(3*2) =\n\n3/6 + 2/6\n\n5/6
928278
if you use the common denominator method , \nyou get\n\n3x/21 = 35/21\n\ntherefore 3x = 35 \n\nx = 35/3\n\n if you cross multiply you will get the exact same thing, but in other cases its not feasible to find the LCD and solve that way. Its not a good approach since you will end up with large fractions.\nlets say for example\n\nx/2773 = 1893/3926 \n \nThe least common denominator for this thing would just be a waste of ink
404835
plug in y\n\n5x-7=8\n5x=15\nx=3
700653
Yes you're correct - just plug in -2 for x to get: \n \n20 - -6 + 1 = 27
1103675
1. convert both to improper fractions\n2. find the least common denominator\n3. multiply both fractions by (x/x) to make the denominator of each the LCD.\n4. subtract the numerators, put the difference over the new LCD.\n5. reduce the fraction\n6. re-convert to mixed numeral\n\n1. 61/8 - 13/3\n2. LCD is 24\n3. (61/8)*(3/3) - (13/3) *(8/8)\n    (183/14) - (104/24)\n4. (183-104)/24\n    79/24\n5. this fraction cannot be reduced\n6. 3 7/24