## anonymous 4 years ago How does x/(x+1) = 1-1/(x+1)

1. anonymous

Do you know about LCM or LCD ???

2. anonymous

you can split up the numerator $\implies \frac{x+1 - 1}{x+1}$ now split up the fraction $\implies \frac{x+1}{x+1} - \frac{1}{x+1}$ does that give you a hint?

3. anonymous

|dw:1346926618139:dw|

4. anonymous

There are two methods for this: Solve RHS to get LHS.. And other is make some arrangements in LHS to get RHS..

5. anonymous

First Method is shown by @chihiroasleaf and second method is shown by @lgbasallote

6. anonymous

If you start with x/(x+1) how can you realize that it equals 1-1/(x+1)/

7. anonymous

like i said $\frac{x}{x+1} \implies \frac{x+1 - 1}{x+1} \implies \frac{x+1}{x+1} - \frac{1}{x+1} \implies 1- \frac 1{x+1}$

8. anonymous

That is what @lgbasallote has shown to you..

9. anonymous

In the numerator if you add and subtract 1 then there is no effect on the equality...

10. anonymous

Oh, so this is almost like multiple the numerator and denominator by x/x (for example).

11. anonymous

yes!!`

12. anonymous

13. anonymous

You got it..

14. anonymous

thanks!

15. anonymous

Welcome dear..