Question 348220
{{{ (4x-1)/(3x+6)-(x-1)/3=(x-1)/(x+2) }}}
Factor
{{{ (4x-1)/(3(x+2))-(x-1)/3=(x-1)/(x+2) }}}
:
{{{(4x-1)/(3(x+2))}}}-{{{(x-1)/3}}} = {{{(x-1)/(x+2) }}}
Multiply by 3(x+2)
3(x+2)*{{{(4x-1)/(3(x+2))}}}-3(x+2)*{{{(x-1)/3}}} = 3(x+2)*{{{(x-1)/(x+2) }}}
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
{{{ (4(2)-1)/(3(2)+6)-(2-1)/3=(2-1)/(2+2) }}}
{{{7/12}}}-{{{1/3}}} = {{{1/4}}}
Common denominator
{{{7/12}}}-{{{4/12}}} = {{{3/12}}}; confirms our solution of x = 2