Question

solve 4÷x-3=5÷2x+3 find the roots

Answer 1

$4 \div x-3=5 \div 2x+3\\ \\ \Rightarrow \frac{4}{x} -3= \frac{5}{2x} +3\\ \\ \Rightarrow \frac{4-3x}{x}= \frac{5+6x}{2x}\\ \\ \Rightarrow 2(4-3x) = 5+6x\\ \\ \Rightarrow 8-6x = 5+6x\\ \\ \Rightarrow 8-5 = 6x+6x\\ \\ \Rightarrow 3 = 12x\\ \\ \Rightarrow x = \frac{3}{12}=\boxed{ \frac{1}{4} }$