Answer:
[tex]3x^2+20x+12=0[/tex]
Justification:
1) The LCD is [tex]2 x^{2} [/tex]
2) The fraction of the left side times the LCD is:
[tex] \frac{x^2-x-6}{x^2} . 2x^2=(x^2-x-6).2=2x^2-2x-12[/tex]
3) the first fraction of the right side times the LCD is:
[tex] \frac{x-6}{2x} .2x^2=(x-6)(x)=x^2-6x[/tex]
4) the second fraction of the right side times the LCD is:
[tex] \frac{2x+12}{x} .2x^2=(2x+12)(2x)=4x^2+24x[/tex]
5) That leads to:
[tex]2x^2-2x-12=x^2-6x+4x^2+24x[/tex]
6) transposing terms to the left and combining like terms:
[tex]2x^2-x^2-4x^2-2x+6x-24x-12=0
-3x^2-20x-12=0
3x^2+20x+12=0[/tex]
