How do you solve the equation 5/x = x-4

x=5

Step-by-step explanation:

write x - 4 as a fraction with denominator = 1

5/x = (x - 4) / 1

Now cross multiply

x (x - 4) = 5 multiply out and collect all terms on the left side of the equal sign

x2 - 4x - 5 = 0 factor the quadratic into two binomials

(x - 5) (x + 1) = 0 the product of two numbers = 0 when either number is zero

Therefore x = 5 or x = - 1