Question

Hello everyone, can you answer this question?
please and thank u
to show that :
1/a+2-1/a+1 :1/a+1-1/a=a/a+2

Answer 1

Answer:

Shown that $\frac{1}{a+2} - \frac{1}{a+1}$ : $\frac{1}{a+1} - \frac{1}{a}$ $=\frac{a}{(a+2)}}$

Step-by-step explanation:

$\frac{1}{a+2} - \frac{1}{a+1}$

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

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

And, $\frac{1}{a+1} - \frac{1}{a}$

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

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

∴ $\frac{1}{a+2} - \frac{1}{a+1}$ : $\frac{1}{a+1} - \frac{1}{a}$

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

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

$=\frac{a}{(a+2)}}$