+0  
 
0
5
1
avatar+1002 

Find all the solutions to
\frac{x+4}{x+5} = \frac{x-3}{2x + 8} - 7.

 Mar 4, 2024
 #1
avatar+128406 
+1

Multiply through by  (x + 5) (2x + 8)

 

(x + 4)(2x + 8)  = (x - 3)(x + 5)  - 7(x+5)(2x + 8)

 

2x^2 + 16x + 32  =  x^2 + 2x -15  - 7 (2x^2 + 18x + 40)

 

2x^2 + 16x + 32 = x^2 + 2x - 15 - 14x^2 - 126x - 280

 

15x^2 + 140x + 327  =  0

 

The solutions  are

 

[-140  +/- sqrt [ 140^2 - 4*15*327] ] / 30    =   [-140 +/- sqrt [ -20 ] ] / 30  =

 

[ -140 +/- 2isqrt (5) ] / 30   =

 

-14/3  +/- (sqrt (5)  / 15)  i

 

cool cool cool

 Mar 4, 2024

1 Online Users

avatar