SOLUTION: Solve (x/6)+((x+4)/2)=(2/(x+5)) I tried multiplying everything by 2(6)(x+5), but then when I tried to factor it, it din't work, I also tried multiplying it by 2(x+5),

Algebra ->  Rational-functions -> SOLUTION: Solve (x/6)+((x+4)/2)=(2/(x+5)) I tried multiplying everything by 2(6)(x+5), but then when I tried to factor it, it din't work, I also tried multiplying it by 2(x+5),       Log On


   

Question 184426: Solve (x/6)+((x+4)/2)=(2/(x+5)) I tried multiplying everything by 2(6)(x+5), but then when I tried to factor it, it din't work, I also tried multiplying it by 2(x+5), but that didn't seem to work either
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve (x/6) + ((x+4)/2) = (2/(x+5))
lcm = 6*(x+5)
-------------------
Multiply thru by the lcm to get:
x(x+5) + 3(x+5)(x+4) = 2*6
x^2 + 5x + 3(x^2 + 9x + 20) = 12
x^2 + 5x + 3x^2 + 27x + 60 = 12
4x^2 + 32x + 48 = 0
x^2 + 8x + 12 = 0
(x+2)(x+6) = 0
x = -2 or x = -6
=======================
Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I think you have the right idea, but here it is step-by-step:
:
Solve %28x%2F6%29%2B%28%28x%2B4%29%2F2%29=%282%2F%28x%2B5%29%29
the common denominator would be 6(x+5), multiply thru by that:
6(x+5)*x%2F6+ 6(x+5)*%28x%2B4%29%2F2 = 6(x+5)*2%2F%28x%2B5%29
:
Cancel out the denominators and you have:
x(x+5) + 3(x+5)(x+4) = 6(2)
:
x^2 + 5x + 3(x^2+ 9x + 20) = 12
:
x^2 + 5x + 3x^2 + 27x + 60 = 12
Combine like terms
x^2 + 3x^2 + 5x + 27x + 60 - 12 = 0
:
4x^2 + 32x + 48 = 0
simplify divide by 4
x^2 + 8x + 12 = 0
Factors to
(x+6)(x+2) = 0
x = -6
x = -2
:
:
Check both solution in original equation
x=-6
%28%28-6%29%2F6%29%2B%28%28-6%2B4%29%2F2%29=%282%2F%28-6%2B5%29%29
%28%28-6%29%2F6%29%2B%28%28-2%29%2F2%29=%282%2F%28-1%29%29
-1 - 1 = -2
:
you can check x=-2