Given the equation:
5−xx−1=92Multiply the equation sides by the denominator 5 - x
we get:
x−5(1−x)(5−x)=910−92xExpand brackets in the left part
1+x5+x-5+x = 10/9 - 2*x/9
Looking for similar summands in the left part:
(1 - x)*(5 - x)/(-5 + x) = 10/9 - 2*x/9
Move free summands (without x)
from left part to right part, we given:
x−5(1−x)(5−x)+5=955−92xMove the summands with the unknown x
from the right part to the left part:
92x+x−5(1−x)(5−x)+5=955Divide both parts of the equation by (5 + 2*x/9 + (1 - x)*(5 - x)/(-5 + x))/x
x = 55/9 / ((5 + 2*x/9 + (1 - x)*(5 - x)/(-5 + x))/x)
We get the answer: x = 19/11