SOLUTION: can someone help me plss before monday? solve the equation. 17. 2x+1/3x-3 = 5x+1/6x-2

Algebra ->  Test -> SOLUTION: can someone help me plss before monday? solve the equation. 17. 2x+1/3x-3 = 5x+1/6x-2      Log On


   



Question 473486: can someone help me plss before monday?
solve the equation.
17. 2x+1/3x-3 = 5x+1/6x-2

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is:
%282x%2B1%29%2F%283x-3%29+=+%285x%2B1%29%2F%286x-2%29
i don't see any common factors, so i think we'll have to do this the hard way.
cross multiply to get:
%282x%2B1%29%2A%286x-2%29+=+%283x-3%29%2A%285x%2B1%29
multiply those factors out to get:
12x%5E2+%2B+2x+-+2+=+15x%5E2+-+12x+-+3
subtract 12x^2 and 2x from both sides of the equation, and add 2 to both sides of the equation to get:
0+=+15x%5E2+-+12x+-+3+-+12x%5E2+-+2x+%2B+2
combine like terms to get:
0+=+3x%5E2+-+14x+-+1
this is the same as:
3x%5E2+-+14x+-+1+=+0
this is a quadratic equation.
you need the quadratic formula to solve this.
the quadratic formula is:
x = -b+%2B-+sqrt%28b%5E2-4ac%29%2F%282a%29
in your equation:
a = 3
b = -14
c = -1
solving by using the quadratic formula gets you:
x = 4.737034184
x = -.070367517
substitute these values of x into the original equations and you will see that the equations are true.
those are your answer.
this was very messy.
i didn't see an easier way to get the answer.