Simplify

**vexiked** · October 2nd 2009, 08:00 AM

How could I simplify

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

**pickslides** · October 2nd 2009, 08:06 AM

Solve or simplify?

**vexiked** · October 2nd 2009, 08:14 AM

Simplify

**Plato** · October 2nd 2009, 08:21 AM

Originally Posted by vexiked

How could I simplify
$\frac{(n+b)}{w+(n+b)}\cdot\frac{b}{w+b}$

As it stands there is no way to simplify the expression.

**ibnashraf** · October 2nd 2009, 08:40 AM

maybe the following might help:

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

so we have,

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

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

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

perhaps someone could verify this ....

**Plato** · October 2nd 2009, 08:46 AM

Originally Posted by ibnashraf

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

Is that a simplification?

**ibnashraf** · October 2nd 2009, 09:16 AM

Originally Posted by Plato

Is that a simplification?

lol, i rather call it a 'complication' compared to the original expression.

my humble apologies though ...

**gs.sh11** · October 2nd 2009, 10:35 AM

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

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

**VonNemo19** · October 2nd 2009, 10:45 AM

Originally Posted by vexiked

How could I simplify

$\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.

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

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.

**pacman** · October 2nd 2009, 05:03 PM

von nemo 19 , ok

**ElectroNerd** · October 3rd 2009, 07:36 AM

$(n+b) / w + (n+b) x b / w + b$

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

**reiward** · October 3rd 2009, 08:26 AM

Originally Posted by ElectroNerd

$(n+b) / w + (n+b) x b / w + b$

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

You cannot cancel the n+b. You cannot cancel terms with an operation sign like (n+b) / w+(n+b)

**ElectroNerd** · October 3rd 2009, 08:29 AM

Does the op have an answer to his question?

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