\( \blacktriangleright \)
Method 1: Using the factor \(\dfrac{1}{15} \)
\(\require{cancel} \dfrac{9-6w}{15}+\dfrac{6w-8}{5} \\ \, \\ =\dfrac{9-6w}{15}+\bigg(\dfrac{6w-8}{5}\cdot\color{red}{\dfrac{3}{3}} \bigg) \\ \, \\ = \dfrac{9-6w}{15}+\dfrac{3(6w-8)}{15} \\ \, \\ = \dfrac{9-6w}{15}+\underbrace{\dfrac{18w-24}{15}}_{\text{Expand}}\\ \, \\ = \dfrac{1}{15}(9-6w+18w-24) \\ \, \\ = \dfrac{1}{15}(12w-15) \\ \, \\ = \dfrac{1}{15}(3)(4w-5)\\ \, \\ = \dfrac{3}{15}(4w-5) \\ \, \\= \dfrac{\cancelto{1}{{\color{red}{3}}}}{\cancelto{5}{{\color{red}{15}}}}(4w-5) \\ \, \\= \dfrac{1}{5}(4w-5) \)
\( \blacktriangleright \)
Method 2: Using the factor \( \dfrac{1}{5} \)
by factoring the first expression first.
\(\require{cancel} \dfrac{9-6w}{15}+\dfrac{6w-8}{5} \\ \, \\ = \bigg(\dfrac{9-6w}{15}\bigg)\bigg(\dfrac{\frac{1}{3}}{\frac{1}{3}}\bigg)+\dfrac{6w-8}{5} \\ \, \\ = \dfrac{3-2w}{5}+\dfrac{6w-8}{5} \\ \, \\ = \dfrac{1}{5}(3-2w+6w-8) \\ \, \\ = \dfrac{1}{5}(4w-5)
\)