Question

(1/x-1)+(1/x-12)=5/4

Answer 1

(1/x-1)+(1/x-12)=5/4
we multiply x-12/x-12 to (1/x-1) and x-1/x-1 to (1/x-12)
this is possible since x-12/x-12 and x-1/x-1are both equal to 1
(1/x-1)(x-12/x-12) + (1/x-12)(x-1/x-1) = 5/4
(x-12/x-1*x-12) + (x-1/x-1*x-12) = 5/4
since the denominators are equal we add the numerators
x-12+x-1/x-1*x-12=5/4
\[2x-13/x ^{2}-13x+12\] =5/4 then we cross multiply,
4(2x-13)=5(\[x ^{2}-13x+12\])
8x-52 = \[5x ^{2}-65x+60\]
\[5x ^{2}-65x+60\]-8x+52= 0
\[5x ^{2}-73x+112\] = 0
in a quadratic equation in the form \[ax ^{2}+bx+c=0\].\[(-b \pm \sqrt{b ^{2}-4ac})\div2a\] gives the two solutions of x.
if you solve the formula the two solutions are 12.85 and 1.74
(you can try it out in a calculator)
hope this helps