SOLUTION: {{{ (4x-1)/(3x+6)-(x-1)/3=(x-1)/(x+2) }}}

Algebra ->  Expressions-with-variables -> SOLUTION: {{{ (4x-1)/(3x+6)-(x-1)/3=(x-1)/(x+2) }}}      Log On


   

Question 348220: +%284x-1%29%2F%283x%2B6%29-%28x-1%29%2F3=%28x-1%29%2F%28x%2B2%29+
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
+%284x-1%29%2F%283x%2B6%29-%28x-1%29%2F3=%28x-1%29%2F%28x%2B2%29+
Factor
+%284x-1%29%2F%283%28x%2B2%29%29-%28x-1%29%2F3=%28x-1%29%2F%28x%2B2%29+
:
%284x-1%29%2F%283%28x%2B2%29%29-%28x-1%29%2F3 = %28x-1%29%2F%28x%2B2%29+
Multiply by 3(x+2)
3(x+2)*%284x-1%29%2F%283%28x%2B2%29%29-3(x+2)*%28x-1%29%2F3 = 3(x+2)*%28x-1%29%2F%28x%2B2%29+
Cancel the denominators:
(4x-1) - (x+2)(x-1) = 3(x-1)
:
4x - 1 - (x^2 + x - 2) = 3x - 3
Remove brackets
4x - 1 - x^2 - x + 2 = 3x - 3
Combine like terms on the left
-x^2 + 4x - x - 3x - 1 + 2 + 3 = 0
-x^2 + 4 = 0
-x^2 = -4
x^2 = +4
x = 2
:
:
Check solution in original problem
+%284%282%29-1%29%2F%283%282%29%2B6%29-%282-1%29%2F3=%282-1%29%2F%282%2B2%29+
7%2F12-1%2F3 = 1%2F4
Common denominator
7%2F12-4%2F12 = 3%2F12; confirms our solution of x = 2