The value of ((3/5)³- (2/5)³)/((3/5)²- (2/5)²) is · ABC26GN1216
Subject: General Aptitude · Chapter: Simplification · Exam: S.S.C. 2003
The value of $\frac{\left(\frac{3}{5}\right)^{3}-\left(\frac{2}{5}\right)^{3}}{\left(\frac{3}{5}\right)^{2}-\left(\frac{2}{5}\right)^{2}}$ is
(a)$\frac{1}{5}$
(b)$\frac{19}{25}$
(c)$\frac{21}{25}$
(d)1
Answer
Explanation
Given $\exp .=\frac{a^{3}-b^{3}}{a^{2}-b^{2}}=\frac{(a-b)\left(a^{2}+a b+b^{2}\right)}{(a-b)(a+b)}=\frac{\left(a^{2}+a b+b^{2}\right)}{(a+b)}$ $$\begin{aligned} & =\frac{\left(\frac{3}{5}\right)^{2}+\left(\frac{3}{5} \times \frac{2}{5}\right)+\left(\frac{2}{5}\right)^{2}}{\left(\frac{3}{5}+\frac{2}{5}\right)} \\ & =\frac{9}{25}+\frac{6}{25}+\frac{4}{25}=\frac{19}{25} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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