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Given $\frac{14x+22}{x+2}=-3x+1$, compute the sum of all the possible values of  Express your answer as a fraction.

I don't know what to do.

 May 17, 2021
 #1
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PANIC

 May 17, 2021
 #2
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nvm  found out it is -19/3 i think

 May 17, 2021
 #3
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[14x  + 22 ]    /   [ x + 2]   =  -3x + 1              multiply  both sides  by  x + 2

 

14x  +  22   =  ( x + 2) ( -3x + 1)     simplify

 

14x  + 22  =  -3x^2 -6x  + x   + 2

 

14x  + 22  = -3x^2  - 5x  + 2     rearrange  as

 

3x^2  + 19x  + 20   =  0           factor  as

 

(3x  + 4 )(x  + 5)   =  0

 

Set  each factor to 0  and solve for  x

 

3x  + 4  = 0              x  + 5   = 0

3x  = -4                     x  =  - 5

x = - 4/3

 

 

cool cool cool

 May 17, 2021

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