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Let \(y = \frac{x - 3}{x + 7}.\)
Then this equation can be expressed in the form \((x + a)(y + b) = c\) for some constants a, b, and c and  Enter your answer in the form "a,b,c  ".

 Apr 27, 2019
 #1
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y  =  (x - 3)  / ( x + 7)                               (x + a)  ( y + b)  =  c

 

y(x + 7)  = x - 3                                         xy + ay + bx + ab =  c  

 

xy +7y  = x - 3                                         xy  + ay  + bx   =  c  - ab  (2)

 

xy + 7y - x  = - 3     (1)

 

Equateing terms in  (1)  and (2)   and we have that

 

a = 7,  b = -1

 

And

 

-3  =  c - ab

-3  = c - (7)(-1)

-3  = c + 7

-10 = c

 

So  { a, b , c }  = { 7, - 1,  -10 }

 

 

cool cool cool

 Apr 27, 2019

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