In the name of Allah, the Beneficent, the Merciful.

Signifying WITHIN the name of Allah is Rahman and Rahim, most tend to forget this

* All praise is due to Allah, + the Lord of the Worlds.
* The Beneficent, the Merciful.
+ Master of the Day of Judgment.

*the link here is
“All praise is due to Allah” and
“The Beneficent, the Merciful.”

+The other link is
“the Lord of the Worlds” and
“Master of the Day of Judgment.”

*Prior ayats explains Allah and that we are within test (and will be judged accordingly)
Then it explains Rahman and Rahim

***Rahman
* Thee do we serve and

***Rahim
+ Thee do we beseech for help.

Now it explains Rahman/Rahim in more detail

***Rahman
Keep us on the right path.

***Rahman
The path of those upon whom Thou hast bestowed favors.

***Rahim
Not (the path) of those upon whom Thy wrath is brought down,

***Rahim
nor of those who go astray.

*the link here is
“Keep us on the right path ” and
“nor of those who go astray “

*the other link is
“The path of those upon whom Thou hast bestowed favors .” and
“Not (the path) of those upon whom Thy wrath is brought down ”

Rahman is defined as – it is active participle noun in the measure of fa’lan which conveys the idea of fullness and extensiveness.

Rahim is defined as – it is in the measure of fa’il which denotes the idea of constant repetition and giving.