Subtract \frac{3n+2}{n-4}-\frac{n-6}{n+4}

(3n+2)/(n-4) - (n-6)/(n+4)

common denominator (n-4)(n+4)

{(n+4)(3n+2)-(n-4)(n-6)}/{(n-4)(n+4)}

Use the foil method:

{(3n²+14n+8)-(n²-10n+24)}/{(n-4)(n+4)}

distribute negative sign:

{(3n²+14n+8-n²+10n-24)}/{(n-4)(n+4)}

subtract:

(2n²+24n-16)/{(n-4)(n+4)}

take out 2:

2{n²+12n-8}/{(n-4)(n+4)}

 

The correct graph is the second one, with the points being at (-6,0), (2,0) and reaching down to (-2,-8)