Multiply the numerator and denominator by the LCD of all of the terms. Distribute it to all the terms. Then factor the polynomials.

$\displaystyle\frac{{{1}+\frac{{4}}{{x}}-\frac{{21}}{{{x}}^{{2}}}}}{{{1}+\frac{{2}}{{x}}-\frac{{35}}{{{{x}}^{{2}}}}}}\cdot\frac{{{{x}}^{{2}}}}{{{{x}}^{{2}}}}=\frac{{{{x}}^{{2}}+{4}{x}-{21}}}{{{{x}}^{{2}}+{2}{x}-{35}}}=\frac{{{\left({x}+{7}\right)}{\left({x}-{3}\right)}}}{{{\left({x}+{7}\right)}{\left({x}-{5}\right)}}}=\frac{{{x}-{3}}}{{{x}-{5}}}\usepackage{cmbright}\Huge\$