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avatar+936 

How do I do this?

 

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

 Dec 15, 2023
 #1
avatar+126978 
+1

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

 

(x + 4) / (x + 5)  =  [ 5(x - 3) + 2(x + 7) ] /  10

 

(x + 4) / (x + 5)  = [ 5x -15 + 2x + 14] / 10

 

(x + 4) / (x + 5)  = [ 7x -1 ] / 10

 

 [ 10 (x + 4)]  - (7x -1) (x+5)] / [10 (x + 5)]     = 0           multiply through by 10(x + 5)

 

[10x + 40  ] - [ 7x^2 +34x -5 ]   =  0

 

-7x^2 - 24x + 45  = 0

 

You can use the quadratic formula to solve this

 

 

cool cool cool

 Dec 16, 2023

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