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This equation can be expressed in the form (x+a)(y+b) = c  for some constants a,b, and c Enter your answer in the form "a,b,c".

 

 

I get this is a rational function and it needs to be changed into a hyperbolic function but I got stuck on how to do that help would be greatly appreciated guys. Thanks for all your hard work on this forum!

 May 11, 2020
 #1
avatar+24951 
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This equation can be expressed in the form \((x+a)(y+b) = c\)  for some constants a,b, and c

 

\(\begin{array}{|rcll|} \hline \mathbf{y} &=& \mathbf{\dfrac{x-3}{x+7}} \\\\ y(x+7) &=& x-3 \\ yx+7y &=& x-3 \\ yx+7y-x &=& -3 \\ x(y-1)+7y &=& -3 \\ x(y-1)+7y-7+7 &=& -3 \\ x(y-1)+7(y-1)+7 &=& -3 \\ x(y-1)+7(y-1) &=& -10 \\ (y-1)(x+7)&=& -10 \\ \mathbf{(x+7)(y-1)} &=& \mathbf{-10} \\ \hline \end{array}\)

 

laugh

 May 11, 2020
 #2
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Thanks for the awesome explanation!

 May 11, 2020

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