If a : b = 5 : 3, then $$(a^3 - b^3) :(a^3+ b^3)$$​ = ?

Correct option is C

Given:

a:b =5:3

Formula Used:

$$\begin {array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\ \hline Brackets &[],{}, () \\ \hline Orders, of & ² (power), √ (root) , of \\ \hline Division & ÷ \\ \hline Multiplication & × \\ \hline Addition & + \\ \hline Subtraction & - \\ \hline \end{array}$$​​

Solution:

​$$\frac{(a^3 - b^3) }{(a^3+ b^3)}$$​​

​$$=\frac{b^3(\frac{a^3}{b^3} - 1) }{b^3(\frac{a^3}{b^3}+ 1)}$$​​

​$$=\frac{(\frac{a^3}{b^3} - 1) }{(\frac{a^3}{b^3}+ 1)}$$​​

​$$=\frac{((\frac{5}{3})^3 - 1) }{((\frac{5}{3})^3+ 1)}$$​​

​$$=\frac{((\frac{125}{27}) - 1) }{((\frac{125}{27})+ 1)}$$​​

​$$=\frac{(\frac{125-27}{27}) }{(\frac{125+27}{27})}$$​​

​$$=\frac{(\frac{98}{27}) }{(\frac{152}{27})}$$​​

​$$=\frac{98}{152}$$​​

​$$=\frac{49}{76} =49:76$$​​