a]
[tex]\frac{3x-3}{x-4}=\frac{x-1}{x+4}\\\\x\neq4, \ x\neq-4\\\\(3x-3)(x+4)=(x-4)(x-1)\\\\3x^2+12x-3x-12=x^2-x-4x+4\\\\3x^2+9x-12=x^2-5x+4\\\\3x^2+9x-12-x^2+5x-4=0\\\\2x^2+14x-16=0 \ \ |:2\\\\x^2+7x-8=0\\\\a=1, \ b=7, \ c=-8\\\\\Delta=7^2-4\cdot1\cdot(-8)=49+32=81\\\\\sqrt{\Delta}=\sqrt{81}=9\\\\x_1=\frac{-7-9}{2}=-8\in\mathbb{D}\\\\x_2=\frac{-7+9}{2}=1\in\mathbb{D}\\\\x=\{-8;1\}[/tex]
b]
[tex]\frac{4x+12}{x^2-9}=\frac{5}{x+5}\\\\x\neq-5, \ x\neq-3, \ x\neq3\\\\5(x^2-9)=(4x+12)(x+5)\\\\5x^2-45=4x^2+20x+12x+60\\\\5x^2-45=4x^2+32x+60\\\\5x^2-45-4x^2-32x-60=0\\\\x^2-32x-105=0\\\\\Delta=(-32)^2-4\cdot1\cdot(-105)=1024+420=1444\\\\\sqrt{\Delta}=\sqrt{1444}=38\\\\x_1=\frac{-(-32)-38}{2}=\frac{-6}{2}=-3\notin\mathbb{D}\\\\x_2=\frac{-(-32)+38}{2}=\frac{70}{2}=35\in\mathbb{D}\\\\x=\{35\}[/tex]
c]
[tex]\frac{x-6}{2x+6}=\frac{3}{7}\\\\x\neq-3\\\\7(x-6)=3(2x+6)\\\\7x-42=6x+18\\\\7x-6x=18+42\\\\x=60[/tex]