x-5/x=25/x+5

Question

Solve the rational equation. Choose the one alternative that best completes the statement or answers that question

A) 25,1

B) 25,-1

C) 5,1

D) 5.-1

Answer 1

Assuming this is the correct equation:

 

(x-5)/x = 25/(x+5)

 

Note that x ≠ 0, -5.

 

Multiply both sides by x(x+5):

 

x(x+5)(x-5)/x = 25x(x+5)/(x+5)

 

(x+5)(x-5) = 25x

 

x^2 - 25 = 25x

 

x^2 - 25x - 25 = 0

 

b^2 - 4ac = 25*25 + 4(25) = 25(25+4) = 25*29

 

x = 25/2 ± 5√(29)/2

 

x ≈ 25.96291201783626, -0.96291201783626 ≈ 26, -1

 

Closest answer is B.

Answer 2

If I got the equation correct

 

x - 5/x  = 25/x  + 5

 

multiply both sides by x

 

x² - 5 = 25 + 5x

 

x² -5x -30 = 0

 

to solve this quadratic equation

 

use formula

 

x = (-b + √(b² - 4.a.c))/2a

 

in this case a = 1, b=-5, c=-30

 

x = (5 +√(5² - (4x1x(-30)))/2

 

x = (5 + √(25+120))/2

 

x= (5 + √(145))/2

 

x = (5 + 12.04)/2

 

x= 8.52 or -3.52

 

:)