2.Where a ≠ 1, (a⁷ - a⁶) / (a - 1) =

A) a/(a -1)
B) 1/(a - 1)
C) a⁶ - a⁵
D) a⁵
E) a⁶

(A) Did you think that a⁷ - a⁶= a¹ = a? Know your math rules. Choice E is correct.

Here's the best way:
Use Strategies 4 and 12, p. 81 and 98; BASIC SKILL - Mini Math Refresher - Algebra, p. 156; Math Refresher (429), p. 257:
When dealing with complicated quantities or equations, it is sometimes simpler to factor to see the quantity take a different form. Factor out a6 from the quantity a⁷ - a⁶. You get a⁶ (a - 1). Thus

a⁷ – a⁶ = a⁶ (a - 1) = a⁶
-----------    ------------
   a - 1          a - 1 

(B) Did you think that a⁷ - a⁶ = 1. Know your math rules. Choice E is correct. Here's the best way:
Use Strategies 4 and 12, p. 81 and 98; BASIC SKILL - Mini Math Refresher - Algebra, p. 156; Math Refresher (429), p. 257:
When dealing with complicated quantities or equations, it is sometimes simpler to factor to see the quantity take a different form. Factor out a6 from the quantity a⁷ - a⁶. You get a⁶ (a - 1). Thus

a⁷ - a⁶ = a⁶ (a - 1) = a⁶
----------    -------------  
  a - 1        a - 1 

(C) Did you think that

a⁷ - a⁶
-----------
 a – 1
would reduce the exponents and you would get a⁶ - a⁵?

Know your math rules. Choice E is correct Here's the best way:
Use Strategies 4 and 12, p. 81 and 98; BASIC SKILL - Mini Math Refresher - Algebra, p. 156; Math Refresher (429), p. 257: When dealing with complicated quantities or equations, it is sometimes simpler to factor to see the quantity take a different form. Factor out a6 from the quantity a⁷ – a⁶. You get a⁶ (a - 1). Thus

a⁷ - a⁶ = a⁶ (a - 1) = a⁶
-----------    -------------  
  a – 1        a – 1 

(D) Know your math rules! Choice E is correct. Here's the best way:
Use Strategies 4 and 12, p. 81 and 98; BASIC SKILL - Mini Math Refresher - Algebra, p. 156; Math Refresher (429), p. 257: When dealing with complicated quantities or equations, it is sometimes simpler to factor to see the quantity take a different form. Factor out a⁶ from the quantity a⁷ – a⁶. You get a⁶ (a - 1). Thus

a⁷ - a⁶ = a⁶ (a - 1) = a⁶
-----------    -------------
   a – 1        a – 1 

(E) You are right! Choice E is correct. And here's the best way:
Use Strategies 4 and 12, p. 81 and 98; BASIC SKILL - Mini Math Refresher - Algebra, p. 156; Math Refresher (429), p. 257: When dealing with complicated quantities or equations, it is sometimes simpler to factor to see the quantity take a different form. Factor out a⁶ from the quantity a⁷ – a⁶. You get a⁶ (a - 1). Thus

a⁷ – a⁶ = a⁶ (a – 1) = a⁶
-----------   -------------- 
  a – 1        a – 1