`4 2/3 : x= 4 4/9 + 1`
`<=> (4xx3+2)/3 : x= (4xx9+4)/9 +1`
`<=> 14/3 : x= 40/9 +1`
`<=> 14/3 : x= 40/9 + 9/9`
`<=> 14/3 : x=49/9`
`<=> x= 14/3 : 49/9`
`<=> x= 14/3 xx 9/49`
`<=>x= 126/147`
`<=>x=6/7`
\(4\dfrac{2}{3}:x=4\dfrac{4}{9}+1\)
\(4\dfrac{2}{3}:x=\dfrac{49}{9}\)
\(x=4\dfrac{2}{3}:\dfrac{49}{9}\)
\(x=\dfrac{6}{7}\)
\(4\dfrac{2}{3}:x=4\dfrac{4}{9}+1\)
\(\dfrac{14}{3}:x=\dfrac{40}{9}+\dfrac{9}{9}\)
\(\dfrac{14}{3}:x=\dfrac{49}{9}\)
\(x=\dfrac{14}{3}:\dfrac{49}{9}=\dfrac{14}{3}\cdot\dfrac{9}{49}\)
\(x=\dfrac{6}{7}\)