Question 785183
Maybe the question was
{{{1/(x-1)+1/(x-5)=3/8}}} which can be typed as 1/(x-1)+1/(x-5)=3/8
 
{{{1/(x-1)+1/(x-5)=3/8}}}
Multiplying both sides by {{{8(x-1)(x-5)}}} to eliminate all denominators, we get
{{{8(x-1)(x-5)(1/(x-1)+1/(x-5))=8(x-1)(x-5)(3/8)}}}
{{{8(x-1)(x-5)/(x-1)+8(x-1)(x-5)/(x-5)=8(x-1)(x-5)3/8}}}
{{{8(x-5)+8(x-1)=3(x-1)(x-5)}}}
{{{8x-40+8x-8=3(x^2-6x+5)}}}
{{{16x-48=3x^2-18x+15}}}
{{{0=3x^2-18x+15-16x+48}}}
{{{3x^2-34x+63=0}}}
 
Armed with a calculator, using the quadratic formula is the most efficient method.
(With only pencil and paper, I would try factoring or completeing the square).
Since the answer was obviously formatted to be entered into a computer directly, a calculator (or equivalent) was available.
 
{{{x= (-(-34) +- sqrt((-34)^2-4*3*63 ))/(2*3) }}}
{{{x= (34 +- sqrt(1156-756))/6}}}
{{{x= (34 +- sqrt(400))/6}}}
{{{x= (34 +- 20)/6}}}
The solutions are:
{{{x[1]= (34 - 20)/6=14/6=highlight(7/3)}}} and
{{{x[1]= (34 + 20)/6=54/6=highlight(9)}}}
 
I would enter the answers as 7/3,9 and hope the computer accepts that.
{Format can be an issue for some small scale online courses).