1. ## Can somebody complete these task?

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.

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

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

Warning the blueprint may be wrong.

2. 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.

3. 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?

4. Hello, Antalya!

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

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

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

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

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

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

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

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

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

5. 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.