# Thread: Prove this

1. ## Prove this

Prove that if x is rational and x≠0, then 1/x is rational.

2. Originally Posted by ilovemymath
Prove that if x is rational and x≠0, then 1/x is rational.
x is rational $\displaystyle \displaystyle\Rightarrow\ x=\frac{a}{b}$

$\displaystyle \displaystyle\frac{1}{x}=\frac{1}{\left(\frac{a}{b }\right)}=\frac{\left(\frac{b}{b}\right)}{\left(\f rac{a}{b}\right)}=\frac{\left(\frac{1}{b}\right)b} {\left(\frac{1}{b}\right)a}$

3. why did you put (b/b)?

4. Originally Posted by ilovemymath
why did you put (b/b)?
To get a common factor in both numerator and denominator.

It helps to arrive at the final fraction since $\displaystyle \frac{b}{b}=1$ and $\displaystyle \displaystyle\frac{\left(\frac{1}{b}\right)}{\left (\frac{1}{b}\right)}=1$

You could also write

$\displaystyle \displaystyle\frac{1}{\left(\frac{a}{b}\right)}=\f rac{b}{b}\frac{1}{\left(\frac{a}{b}\right)}=\frac{ b}{a}$

5. ya but eventually lets say a=1,b=2... at the end you will get the answer (1/(1/2)) and if u simplyfy is it will give u the anser 2... which is not rational

6. Originally Posted by ilovemymath
ya but eventually lets say a=1,b=2... at the end you will get the answer (1/(1/2)) and if u simplyfy is it will give u the anser 2... which is not rational
$\displaystyle 2=\frac{2}{1}=\frac{4}{2}=\frac{6}{3}=.......$

2 is rational.

7. ohhhk thnknss