Question 122408
x+6 x
--- = ---
x+2 x-1
:
{{{((x+6))/((x+2))}}} = {{{x/((x-1))}}}
:
Cross multiply
(x+6)(x-1) = x(x+2)
:
FOIL (x+6)(x-1)
x^2 + 5x - 6 = x^2 + 2x
:
Combine like terms on the left:
x^2 - x^2 + 5x - 2x - 6 = 0
3x - 6 = 0
3x = +6; added 6 to both sides
x = {{{6/3}}}
x = +2
:
Check solution in original equation, substitute 2 for x
{{{((x+6))/((x+2))}}} = {{{x/((x-1))}}}
{{{((2+6))/((2+2))}}} = {{{2/((2-1))}}}
{{{((8))/((4))}}} = {{{2/((1))}}}; proves our solution of x=2