1. ## Simplify

How could I simplify

$\displaystyle \frac{(n+b)}{w+(n+b)}\cdot\frac{b}{w+b}$

2. Solve or simplify?

3. Simplify

4. Originally Posted by vexiked
How could I simplify
$\displaystyle \frac{(n+b)}{w+(n+b)}\cdot\frac{b}{w+b}$
As it stands there is no way to simplify the expression.

5. maybe the following might help:

try using a substitution: a = (n + b),

so we have,

$\displaystyle \frac{a}{(w+a)}$.$\displaystyle \frac{b}{(w+b)}$

multiply out the denominator and then re-substitute for 'a' and simplify

i ended up with $\displaystyle \frac{b(n+b)}{(w+b)((w+b)^2 + n)}$

perhaps someone could verify this ....

6. Originally Posted by ibnashraf
i ended up with $\displaystyle \frac{b(n+b)}{(w+b)((w+b)^2 + n)}$
Is that a simplification?

7. Originally Posted by Plato
Is that a simplification?
lol, i rather call it a 'complication' compared to the original expression.

my humble apologies though ...

8. ## Cross Multiply

I think simplify means to cross multiply.
$\displaystyle \frac{(n+b)}{w+(n+b)}\cdot\frac{b}{w+b}$

cross multiply and you will get:
$\displaystyle (n+b)(w+b)=b[w+(n+b)]$

9. Originally Posted by vexiked
How could I simplify

$\displaystyle \frac{(n+b)}{w+(n+b)}\cdot\frac{b}{w+b}$
Perhaps if we rewrite, it will become apparent that this thing is factored as nicely as possible.

$\displaystyle \frac{(n+b)}{w+(n+b)}\cdot\frac{b}{w+b}=\frac{b(n+ b)}{(w+b)(w+n+b)}$

Note that

1. Nothing cancels

2. there is no way to factor any more completely.

Therefore, this quotient is in its simplest form.

If you apply those two rules, you'll never have these questions again.

10. von nemo 19 , ok

11. $\displaystyle (n+b) / w + (n+b) x b / w + b$

Notice above that $\displaystyle (n+b)$ can cancel out leaving us with $\displaystyle 1 / w$ Now, multiply that by $\displaystyle b / w+b$, and I think it becomes $\displaystyle b / w^2 + wb$. Then, b cancels out and I think we're left with $\displaystyle 1 / w^2 + w$

12. Originally Posted by ElectroNerd
$\displaystyle (n+b) / w + (n+b) x b / w + b$

Notice above that $\displaystyle (n+b)$ can cancel out leaving us with $\displaystyle 1 / w$ Now, multiply that by $\displaystyle b / w+b$, and I think it becomes $\displaystyle b / w^2 + wb$. Then, b cancels out and I think we're left with $\displaystyle 1 / w^2 + w$
You cannot cancel the n+b. You cannot cancel terms with an operation sign like (n+b) / w+(n+b)

13. Does the op have an answer to his question?