Answer:
[tex]\sf \dfrac{8}{21}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x}[/tex]
When multiplying fractions, simply multiply the numerators and multiply the denominators:
[tex]\implies \sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x} = \dfrac{6x \cdot 4}{-7 \cdot -9x} =\dfrac{24x}{63x}[/tex]
Cancel the common factor x:
[tex]\implies \sf \dfrac{24 \diagup\!\!\!\!x}{63 \diagup\!\!\!\!x}=\dfrac{24}{63}[/tex]
Rewrite 24 as 3 · 8 and rewrite 63 as 3 · 21:
[tex]\implies \sf \dfrac{24}{63}=\dfrac{3 \cdot 8}{3 \cdot 21}[/tex]
Cancel the common factor 3:
[tex]\implies \sf \dfrac{\diagup\!\!\!\!\!3 \cdot 8}{\diagup\!\!\!\!\!3 \cdot 21}=\dfrac{8}{21}[/tex]
