Question 167553
{{{ (1/(1+x)) - (1/(3-x)) = 6/35 }}}
Multiply both sides by a common denominator of 35(1+x)(3-x):
{{{ (35(3-x)) - (35(1+x)) = 6(1+x)(3-x) }}}
Expanding:
{{{ (105-35x) - (35+35x)) = 6(3-x+3x-x^2) }}}
{{{ 105-35x-35-35x = 6(3+2x-x^2) }}}
{{{ 70-70x = 18+12x-6x^2 }}}
{{{ 6x^2+70-70x = 18+12x }}}
{{{ 6x^2-82x+70 = 18 }}}
{{{ 6x^2-82x+52 = 0 }}}
{{{ 3x^2-41x+26 = 0 }}}
{{{ (3x-2)(x-13) = 0 }}}
.
Two possible solutions:
3x-2=0
3x = 2
x = 2/3
.
x-13 = 0
x = 13
.
x = {2/3, 13}