Question 950246
Assume the equation is:
{{{((x-1))/((x-5)) - 1/5 = 20/((x^2-5x))}}}
Factor out x
{{{((x-1))/((x-5)) - 1/5 = 20/(x(x-5))}}}
multiply by the common denominator 5x(x-5)
5x(x-5)*{{{((x-1))/((x-5))}}} - 5x(x-5)*{{{1/5}}} = 5x(x-5)*{{{20/(x(x-5))}}}
cancel the denomonators
5x(x-1) - x(x-5) = 5(20)
5x^2 - 5x - x^2 + 5x = 100
Combine like terms
5x^2 - x^2 - 5x + 5x = 100
4x^2 = 100
x^2 = 100/4
x^2 = 25
x = +/-{{{sqrt(25)}}}
x = 5
or
x =-5
:
x = 5 cannot be a solution, we would have division by 0 in the original problem
however
x = -5 seems to work ok in the original problem, only solution