Precalculus: Mathematics for Calculus, 7th Edition

$\dfrac{x+1}{x-1}=\dfrac{3x}{3x-6}$ Take $x-1$ to multiply the right side and $3x-6$ to multiply the left side: $(x+1)(3x-6)=3x(x-1)$ Evaluate the products on both sides: $3x^{2}-6x+3x-6=3x^{2}-3x$ Evaluate the operations on both sides: $3x^{2}-3x-6=3x^{2}-3x$ Take all terms to the left side: $3x^{2}-3x-6-3x^{2}+3x=0$ Simplify the left side: $-6\ne0$ This equation has no solution