Chapter 6 - Sections 6.1-6.5 - Integrated Review - Expressions and Equations Containing Rational Expressions - Page 380: 18

$x=-\dfrac{3}{13}$

By cross-multiplication, the solution to the given equation, $ \dfrac{5x-3}{2x}=\dfrac{10x+3}{4x+1} ,$ is \begin{array}{l} (5x-3)(4x+1)=2x(10x+3) \\\\ 20x^2+5x-12x-3=20x^2+6x \\\\ (20x^2-20x^2)+(5x-12x-6x)=3 \\\\ -13x=3 \\\\ x=\dfrac{3}{-13} \\\\ x=-\dfrac{3}{13} .\end{array}