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Find all values of c such that c/(c - 5) = 4/(c - 1). If you find more than one solution, then list the solutions you find separated by commas.

 Oct 24, 2020
 #1
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Solve for c:
c/(c - 5) = 4/(c - 1)

Cross multiply:
c (c - 1) = 4 (c - 5)

Expand out terms of the left hand side:
c^2 - c = 4 (c - 5)

Expand out terms of the right hand side:
c^2 - c = 4 c - 20

Subtract 4 c - 20 from both sides:
c^2 - 5 c + 20 = 0

Subtract 20 from both sides:
c^2 - 5 c = -20

Add 25/4 to both sides:
c^2 - 5 c + 25/4 = -55/4

Write the left hand side as a square:
(c - 5/2)^2 = -55/4

Take the square root of both sides:
c - 5/2 = (i sqrt(55))/2 or c - 5/2 = -(i sqrt(55))/2

Add 5/2 to both sides:
c = 5/2 + (i sqrt(55))/2 or c - 5/2 = -(i sqrt(55))/2

Add 5/2 to both sides:
c = 5/2 + (i sqrt(55))/2                       or                          c = 5/2 - (i sqrt(55))/2

 Oct 24, 2020

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