Solve 5 over x minus 5 equals the quantity of x over x minus 5, minus five fourths for x and determine if the solution is extraneous or not

ANSWER

The solution

is extraneous.

EXPLANATION

The given equation is



We multiply the above equation with the least common multiple of denominators which is


This implies that,



This simplifies to





This implies that,



Therefore


But this solution does not satisfy the original equation.





Hence

is an extraneous solution.