Can somebody complete these task?

**Antalya** · December 4th 2010, 04:55 AM

Shorten the rational expressions as possible.

a) $\frac{x^{2}+4x+4}{x^{2}-4}$

b) $\frac{x^{2}+x-6}{x^{2}-2x}*\frac{6x}{2x^{2}-18}$

I need full calculation with these task and the answer must be in order and complete.

The answer:

a) $\frac{x+2}{x-2}$

b) $\frac{3}{x-3}$

Warning the blueprint may be wrong.

Than you for your help.

**earboth** · December 4th 2010, 05:06 AM

Originally Posted by Antalya

Shorten the rational expressions as possible.

a) $\frac{x^{2}+4x+4}{x^{2}-4}$
...
I need full calculation with these task and the answer must be in order and complete.

...

1. Factor the numerator and the denominator of this quotient.

2. Cancel equal terms.

3. The numerator is a complete square and the denominator is a difference of squares which can be factored easily.

4. The given answer is correct.

**Antalya** · December 4th 2010, 05:13 AM

The problem that is i don't know how to do the task. It is impossible for me to do those because I have low skill in math and I would be very happy if you or someone else could do those?

**Soroban** · December 4th 2010, 05:25 AM

Hello, Antalya!

You've never reduced a fraction before . . . ever?

Factor all expressions, then reduce (cancel) as much as possible.

$\text{(a) Simplify: }\:\dfrac{x^2+4x+4}{x^2-4}$

$\displaystyle \text{Factor: }\:\frac{(x+2)(x+2)}{(x-2)(x+2)}$

$\displaystyle \text{Reduce: }\;\frac{(x+2)(\rlap{/////}x+2)}{(x-2)(\rlap{/////}x+2)} \;=\;\frac{x+2}{x-2}$

$\text{(b) Simplify: }\:\dfrac{x^2+x-6}{x^2-2x}\cdot \dfrac{6x}{2x^2-18}$

$\displaystyle\text{Factor: }\;\frac{(x-2)(x+3)}{x(x-2)} \cdot \frac{6x}{2(x-3)(x+3)}$

$\displaystyle \text{Reduce: }\;\frac{(\rlap{/////}x-2)(\rlap{/////}x+3)}{x(\rlap{/////}x-2)} \cdot\frac{6x}{2(x-3)(\rlap{/////}x+3)}$

. . . . . . . $\displaystyle =\;\frac{1}{\rlap{/}x} \cdot \frac{\rlap{/}6^{^3}\rlap{/}x}{\rlap{/}2(x-3)} \;=\; \frac{3}{x-3}$

**mr fantastic** · December 4th 2010, 12:18 PM

Originally Posted by Antalya

The problem that is i don't know how to do the task. It is impossible for me to do those because I have low skill in math and I would be very happy if you or someone else could do those?

Then you need to ask for extra help from your teacher. Giving you the complete solutions to these questions will not change your "low skill in math", extra help from your teacher might.

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