i have tried my best to ans if wrong really very very very very very very heartly sorry pleaae please forgive me its just a try have great day be happy and smilling :)

Verified answer

[tex] \sf \: value \: of \: : \\ \sf \: \dfrac{ {a }^{3 } + {b}^{3} - 3abc }{ab + bc + ca - ( {a}^{2} + {b}^{2} + {c}^{2}) } \: \: is \: \: \boxed{\sf \dfrac{533}{112} } \\ [/tex]

Step-by-step explanation:

Given :

• a = 7
• b = -5
• c = 3

To find :

[tex] \boxed{\sf \: \dfrac{ {a }^{3 } + {b}^{3} - 3abc }{ab + bc + ca - ( {a}^{2} + {b}^{2} + {c}^{2} )} } \\ [/tex]

Solution :

[tex] \sf \: put \: the \: above \: values \: of \: a \: b \: and \: c \: .[/tex]

[tex] \sf \: let \: \sf \: \dfrac{ {a }^{3 } + {b}^{3} - 3abc }{ab + bc + ca - ( {a}^{2} + {b}^{2} + {c}^{2} )} = \bf x \\ \\ \\ \sf x\: = \: \dfrac{ {(7)}^{3} + { (- 3)}^{3} - (3 \times 7 \times ( - 5) \times 3 }{7 \times ( - 5) + ( - 5) \times 3 - \{ {(7)}^{2} + {( - 5)}^{2} + {(3)}^{2} } \\ \\ \\ \sf x\: = \: \frac{343 - 125 + 315}{ - 35 - 15 + 21 - (49 + 25 + 9)} \\ \\ \tt \: after \: solving \:it \: we \: get.... - \: \\ \\ \: \boxed{\sf x = \dfrac{533}{112} } \\ [/tex]

[tex]\rule{190pt}{2pt} \\ [/tex]