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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.

 Dec 16, 2020
 #1
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c / ( c - 5)  =  4 / (c - 1)     cross-multiply

 

c ( c - 1)  =  4(c - 5)

 

c^2  - c   = 4c - 20

 

c^2 - c - 4c + 20   =   0

 

c^2  - 5c  +  20    =  0         complete the square on c

 

c^2 - 5c + 25/4   =  - 20 + 25/4

 

(c - 5/2)^2   =  -55/4       take  both roots

 

c - 5/2   =   ± i sqrt ( 55) / 2

 

c =     5/2  ± i sqrt (55)  /2

 

 

cool cool cool

 Dec 16, 2020

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