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

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

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Westford, MA

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.

Tracy, CA

If I got the equation correct

x - 5/x = 25/x + 5

multiply both sides by x

x^{2} - 5 = 25 + 5x

x^{2} -5x -30 = 0

to solve this quadratic equation

use formula

x = (-b + √(b^{2} - 4.a.c))/2a

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

x = (5 +√(5^{2} - (4x1x(-30)))/2

x = (5 + √(25+120))/2

x= (5 + √(145))/2

x = (5 + 12.04)/2

x= 8.52 or -3.52

:)

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