Question

If a/b = 2/3
Then find
(1) a²+b² / a²-b²
(2) 2a³-b³/b³

Answer 1

Answer:

(1) $\frac{-13}{5}$

(2) $\frac{-11}{27}$

Step-by-step explanation:

(a)

       $\frac{a^2+b^2}{a^2-b^2}$

Dividing each term by $b^2$

                  $\frac{(\frac{a}{b})^2+(\frac{b}{b} )^2 }{(\frac{a}{b} )^2-(\frac{b}{b})^2 } \\ \\ \\ =\frac{(\frac{a}{b})^2+1}{(\frac{a}{b})^2-1}$

Putting the value of $\frac{a}{b} =\frac{2}{3}$

                          $\frac{(\frac{2}{3})^2+1 }{(\frac{2}{3} )^2-1} \\ \\ =\frac{4+9}{4-9} \\ \\ =\frac{-13}{5}$

(b)

                                 $\frac{2a^3-b^3}{b^3} \\ \\ 2(\frac{a}{b})^3-1\\ \\ =2(\frac{8}{27})-1\\ \\ \frac{16-27}{27} \\ \\ =\frac{-11}{27}$