Question 262817
Here is the original problem:
(i) {{{(x+(2/x))/(7-(2/x))=6x}}}
step 1 - cross multiply to get
(ii) {{{x+ (2/x) = 42x -12}}}
step 2 - multiply by x to get
(iii) {{{x^2 + 2 = 42x^2 - 12x}}}
step 3 - set = 0 to get
(iv) {{{0 = 41x^2 - 12x - 2}}}
step 4 - by the quadratic, we get
{{{x = (12 +- sqrt( 144-4*41*(-2) ))/(82) }}}
which is
{{{x = (12 +- sqrt( 472))/(82) }}}
and then
{{{x = (12 +- 2sqrt( 118))/(82) }}}
and reducing, we get
{{{x = (6 +- sqrt( 118))/(41) }}}