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# x-5/x=25/x+5

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

### 2 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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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

Amarjeet K. | Professional Engineer for Math and Science TuroringProfessional Engineer for Math and Scien...
4.6 4.6 (8 lesson ratings) (8)
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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

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

:)