Question

(9x-7)/(3x+5)=(3x-4)/(x+6) find the value of x

Answer 1

`D:\\3x+5\\eq0\ \wedge\ x+6\\eq0\to x\\eq-(5)/(3)\ \wedge\ x\\eq-6\\\\(9x-7)/(3x+5)=(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=(22)/(44)\\\\\boxed{x=(1)/(2)}\in D`