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Find all values of x such that  2x/(x - 2) = -6/(x + 4).
If you find more than one value, then list your solutions, separated by commas.

 Jan 19, 2021
 #1
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2x / ( x - 2)  = -6/ ( x + 4)     cross-multiply

 

2x ( x + 4)   =  -6 ( x  - 2)         simplify

 

2x^2 + 8x  = -6x   +  12        rearrange as

 

2x^2 + 14x  - 12   =  0          divide through  by 2

 

x^2 + 7x   - 6  = 0            add 6 to both sides

 

x^2  +  7x   =   6

 

Complete the square on  x

 

Take 1/2  of 7 =  7/2      square this =  49/4and add to both sides

 

x^2  +  7x    + 49/4   =  6 +  49/4      factor the left side, simplify the  right

 

(x + 7/2)^2  =  73/4              take both roots

 

x + 7/2  =    ±√73/2        subtract 7/2 from  both sides

 

x =   ±√73/2  - 7/2

 

 

cool cool cool

 Jan 19, 2021

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