how do i solve 5/x= x-4 ?

Question

please help!!

Answer 1

5/x = x - 4



multiply both sides by x:



5 = x^2 - 4x



rewrite as quadratic equation:



x^2 - 4x - 5 = 0



factor:



(x - 5)(x + 1) = 0



apply zero-product property:

x - 5 = 0 or x + 1 = 0



solve each equation:



x = 5 or x = -1



that's it! ;)

Answer 2

5/x=x-4

add four to both sides

4+5/x=x

multiply x to both sides to get rid of the fraction

4+5=x^2

9=x^2

square root of 9 is 3

x=3