How do i prove equation

[totalNoob]

Hi (my english not so very good)
I know that these 2 fractions are equal but i don't know how to show that
this
and this
I will be greatfull for any help

 

[Romsek]

I'd start by dividing top and bottom by (x+2) and see what that gets you.

 

[Otis]

Hello. (2x + 2) needs to be factored, too.

Remembering the special factoring pattern known as a 'Difference of Squares' will also help, in the numerator, after you first cancel the common factors x+2.

Note: Canceling the common factors x+2 is the same as dividing by x+2 on top and bottom, suggested by Romsek, so you're free to write out the process either way.

\(\displaystyle \frac{(x + 2)^3 - (x + 2)}{(x + 2)^2 (2x + 2)}\)

When we examine that algebraic ratio symbolically, we see this form:

\(\displaystyle \frac{a^3 - a}{a^2 \cdot b}\)

We cancel common factors of a:

\(\displaystyle \frac{a^2 - 1}{a \cdot b}\)

Or, using Romsek's suggestion to divide top and bottom by a:

\(\displaystyle \frac{a^3 - a}{a} \quad \text{and} \quad \frac{a^2 \cdot b}{a}\)

also yields \(\frac{a^2 - 1}{a \cdot b}\)

Let us know, if you need help understanding the suggestions. Please also show any work that you've tried. Cheers

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[totalNoob]

Thank you. The point for me was to understand that (2x+4)=2(x+2) then i have almost the same denominator in both fractions and the rest is esay.

 

[Otis]

... The point for me was to understand that (2x+4)=2(x+2) ...

I see. When working with algebraic ratios, a good first step is to factor every part that we can -- even if that turns out to be partly unneccessary -- just so we can see all of the sub-parts.

Good job, finding your answer.

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