Search 74,172 tutors
FIND TUTORS
Ask a question
0 0

x-5/x=25/x+5

Tutors, please sign in to answer this question.

2 Answers

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.
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
 
:)

Woodbridge Algebra tutors