[tex]D:\\3x+5\neq0\ \wedge\ x+6\neq0\to x\neq-\frac{5}{3}\ \wedge\ x\neq-6\\\\\dfrac{9x-7}{3x+5}=\dfrac{3x-4}{x+6}\ \ \ \ |cross\ multiply\\\\(9x-7)(x+6)=(3x+5)(3x-4)\\9xx+(9x)(6)-7x-(7)(6)=(3x)(3x)-(3x)(4)+(5)(3x)-(5)(4)\\9x^2+54x-7x-42=9x^2-12x+15x-20\\9x^2+47x-42=9x^2+3x-20\ \ \ \ |subtract\ 9x^2\ from\ both\ sides\\47x-42=3x-20\ \ \ |add\ 42\ to\ both\ sides\\47x=3x+22\ \ \ |subtract\ 3x\ from\ both\ sides\\44x=22\ \ \ \ |divide\ both\ sides\ by\ 44\\x=\dfrac{22}{44}\\\\\boxed{x=\dfrac{1}{2}}\in D[/tex]
