x/x^2-9-x+4/x^2-3x=-6/x^2+3x

Question

This is for my Math 126 course please someone helpppp!!!

Answer 1

x²-9=(x-3)(x+3); x²-3x=x(x-3); x²+3x=x(x+3). Multiply through by (x-3)(x+3):

x(x-3)(x+3)/(x²-9)-(x+4)(x-3)(x+3)/[x(x-3)]=-6(x-3)(x+3)/[x(x+3)],

which simplifies through cancellation:

x-(x+4)(x+3)/x=-6(x-3)/x, multiply through by x:

x²-(x²+7x+12)=-6x+18,

-7x-12=-6x+18,

-30=x, so x=-30.