how would you solve 5/x=x-4

Question

math

 

Answer 1

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