Question

Simplifying Complex Fractions? Help anyone please

Answer 1

\(\bf \cfrac{\frac{18x-6}{9x^5}}{\frac{15x+5}{21x^2}}\quad \textit{getting common factors}\\ \quad \\
\cfrac{\frac{6(3x-1)}{9x^5}}{\frac{5(3x+1)}{21x^2}}\qquad \textit{recall that }\cfrac{\quad \frac{a}{b}\quad }{\frac{c}{d}}\implies \cfrac{a}{b}\cdot \cfrac{d}{c}\qquad thus\\ \quad \\
\cfrac{\frac{6(3x-1)}{9x^5}}{\frac{5(3x+1)}{21x^2}}\implies \cfrac{6(3x-1)}{9x^5}\cdot \cfrac{21x^2}{5(3x+1)}\implies

\cfrac{\cancel{3}\cdot 2(3x-1)}{\cancel{3}\cdot \cancel{3}\cancel{x^5}}\cdot \cfrac{\cancel{3}\cdot 7\cancel{x^2}}{5(3x+1)}\)

Answer 2

the final answer is 2(3x-1)/5(3x+1)