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 ".
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 }