Question

Please solve this question I need it...​

Answer 1

Given: $x=\dfrac{2}{5},y=\dfrac{-4}{3},z=\dfrac{8}{9}$

Left hand side

$=x+(y+z)$

$=\dfrac{2}{5}+(\dfrac{-4}{3}+\dfrac{8}{9})$

$=\dfrac{2}{5}+\dfrac{-4\times 3+8\times 1}{9}$

$=\dfrac{2}{5}+\dfrac{-12+8}{9}$

$=\dfrac{2}{5}+\dfrac{-4}{9}$

$=\dfrac{2\times 9+(-4)\times 5}{45}$

$=\dfrac{18-20}{45}$

$=\dfrac{-2}{45}$

Right hand side

$=(x+y)+z$

$=(\dfrac{2}{5}+\dfrac{-4}{3})+\dfrac{8}{9}$

$=\dfrac{2\times 3+(-4)\times 5}{15}+\dfrac{8}{9}$

$=\dfrac{6-20}{15}+\dfrac{8}{9}$

$=\dfrac{-14}{15}+\dfrac{8}{9}$

$=\dfrac{(-14)\times 3+8\times 5}{45}$

$=\dfrac{-42+40}{45}$

$=\dfrac{-2}{45}$

Thus, $x+(y+z)=(x+y)+z$ is satisfied.