- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
If $\frac{1}{b} \div \frac{b}{a} = \frac{a^2}{b}$, where a, b not equal to 0, then find the value of $\frac{\frac{a}{(\frac{1}{b})} - 1}{\frac{a}{b}}$.
Given :
$ \frac{1}{b} \div \frac{b}{a} =\frac{a^{2}}{b}$ , a, b not equal to 0.
To find :
We have to find the value of $\frac{\frac{a}{(\frac{1}{b})} - 1}{\frac{a}{b}}$.
Solution :
$\frac{1}{b} \times \frac{a}{b} =\frac{a^{2}}{b}$
$a\times b=a^{2} \times b^{2}$
$ab=a^{2} b^{2}$
$ab( ab-1) =0$
$ab=0\ or\ ab=1$
$ab \ not \ equal \ to \ 0 $ [since a not equal to 0 and b not equal to 0]
Therefore,
$ab = 1.$
$\frac{\frac{a}{1/b} -1}{\frac{a}{b}} \ =\ \frac{\frac{a-\left(\frac{1}{b}\right)}{1/b}}{a/b}$
$=\frac{a-\left(\frac{1}{b}\right)}{1/b} \times \frac{b}{a}$
$ =\ \frac{( ab-1) /b}{1/b} \times \frac{b}{a}$
$ =\ \frac{b( ab-1)}{a}$
$ =\frac{b( 1-1)}{a}$
$=0$
Therefore, the value of $\frac{\frac{a}{(\frac{1}{b})} - 1}{\frac{a}{b}}$ is $0$.