Simplify: x + 4y/y//x+y/y?
831251
This problem is kind of neat. We have two fractions in a compound fraction - one in the numerator and one in the denominator. Since both fractions have the same denominator:\n\n(x + 4y)/y and (x + y)/y\n\nWe can eliminate the y's and form a fraction out of the numerators. Note that we can only do this because the denominators are the same.\n\nSo the original expression equals:\n\n(x + 4y)/(x + y)\n\nAnother way to do this is to multiply the fraction in the numerator by the reciprocal of the fraction in the denominator.\n\n(x + 4y)/y * y/(x + y) =  y(x + 4y) / y(x + y) = (x + 4y) / (x + y)
386537
4y=3x\ny=3x/4\ny=3/4 x\n\nGet it?
586962
(6y^2-3y)(y+7)-->(2y)(y-1)(y+7)\nif that helps
804813
(y+1)(y-7)\n=y^2-6y-7
564627
change the equation to slope intercept form\nsolve the equations for y\nx+2y=3\n2y= 3- x\ny= -x/2 + 3/2\nDo the same thing for the other formula\nthe form is\ny = mx + b\nAfter that just plug in numbers for x to get y
982897
the 1st one is simple\n(x+y) dy/dx + y =0\nor xdy/dx + ydy/dx + y =0\nor (xdy/dx + y)  + ydy/dx = 0\nxdy/dx + y = d/dx(xy)\n\nand d(y^2/2)/dx \n\nso d/dx(xy+y^2/2) = 0\n\nor xy+y^2/2 = c\nor 2xy+y^2 = 2c or C\n\nproved\nfor the second one\n\ndy/dx -(1/x)y = xy^2\n\nlet y/x = t\ny = xt\ndy/dx -y/x = t+ x dt/dx -t = x dt/dx\nso\nx dt/dx = - x (xt)^2\nor dt/dx = x^2t^2\ndt/t^2 = x^2 dx\nyou should be able to proceed
959758
( -1 -y) / (x + 4y) = -1/3\n=> (1 + y) = (x + 4y)/3\n=> 3 + 3y = x + 4y\n=> x + y = 3 => x = 3 - y = k  =>\nx = k\ny = 3 - k\n\nit means,for infinite number of k,x = k and y = 3 - k
439090
((x^2-2x)/4y)/((x^2-4)/6)\n=(6x(x-2))/(4y*(x-2)(x+2))\n=3x/(2y(x+2))
708981
(4/x-8/y)/(24/xy)\n=(4y-8x/xy) * xy/24\n= 4(y-2x)/xy * xy/24\n=(y-2x)/6
818222
1.) (x^2y)/(xy) = ((x)(x)(y))/(x)(y) = (x/x)(y/y)(x) = (1)(1)(x) = x\n\n2.) (3(x-2)^2)/(6(x-2)^4) = ((3)(x-2)(x-2))/((3)(2)(x-2)(x-2)(x-2)^2)\n    *Now what can be "1" \n\n3.) There may be a type-o in the denom having the "+" sign, but if such the case, the expression is at it's simplest form.\n\n4.) Now for this think about factoring out a number and I think you'll see something that can be in its simplest form.
728358
Just divide through by 3 to get the y alone\n\n3y = 2x + 3\n\n3y /3 = 2x/3 + 3/3\ny = (2/3)x + 1
957836
4x+(-5y)+(-6x)+3y\n4x+(-6x)+(-5y)+3y\n=-2x-2y
712820
write them so they can be added top to bottom (i.e. line up the x's, y's, and constants):\n\n4x + 2y = -4\nx - 2y = -3  (we need to rearrange the original equation here to line things up)\n\nnow add top to bottom:\n\n(4x)+(x)  +  (2y)+(-2y)  =  (-4)+(-3)\n5x + 0 = -7\n5x = -7\nx = -7/5\n\nnow plug x in to either equation to solve for y:\n\n2y = -7/5 + 3\n2y = -22/3\ny = -22/6 = -11/3\n\nHope this helps :)
356024
x + y + z = t\n\nx +x% + y + y% + z + z% =\n[(100 + 1)( x + y + z)]% =\n101t% = t + t%. So\nx +x% + y + y% + z + z% = = t + t% or\nx% + y% + z% = t%
539943
x+y........e=mc2..........2+2
963003
int(y+2/2y^2+3y+1 dy)\n\n1/2*y^2 - 1/y + 3/2*y^2 + y + c\n\n2*y^2 - 1/y + y + c
718048
x + y = 3\n\nSolve for a variable.  I chose X.\nx+y = 3\n -y    -y\nx = 3 - y\n\nSubstitute the value of X in the first equation.\n2(3-y) + y = 4\nDistribute.\n6-2y+y = 4\nAdd like terms.\n6-y = 4\n-6    -6\n-y = -2\nmultiply by -1.\ny=2\n\nSince you know Y = 2, substitute that back into the second equation that you solved for X with.\nx + y = 3\nX + 2 = 3\n  -2    -2\nX = 1\n\nX = 1\nY = 2