Answer:

Activity 1:

1.  NS. Simplest form: 2b / a

5. S

6. S

Activity 2:

2. -1

3.  [3 (4a - 7)] / [4 (3a - 7)]

5. (a + 1) / (a + 3)

Step-by-step explanation:

Activity 1

1.

(8b^2) / 4ab    

(Divide b^2/b and divide 8/4)

= 2b / a

5.

(x^2 + 4x + 3) / (x^2 +6x + 8)    

(Factor out the numerator and denominator)

= [ (x + 3) (x + 1) ] / [ (x + 4) (x + 2) ]

(The equation is already in simplest term since no factors can be cancelled)

6.

(3b^2 - a) / (3a - b^2)

= (3b^2 - a) / [-1 (b^2 - 3a)]

(The equation is already in simplest term)

Activity 2

2.

(4a - 1) / (1 - 4a)

= (4a - 1) / [-1 (4a - 1)]

(Factor out negative 1 from the denominator. Then cancel out 4a -1)

= 1 / (-1)

= -1

3.

(12a^2 - 21a) / (12a^2 - 28a)

(Factor out 3a from the numerator. And factor out 4a from the denominator)

= [3a (4a - 7)] / [4a (3a - 7)]

(Cancel out a)

= [3 (4a - 7)] / [4 (3a - 7)]

5.

(2a^2 - 2) / (2a^2 + 4a - 6)

(Factor out 2 from the numerator)

= [2 (a^2 - 1)] / [2 (a^2 + 2a - 3)]

(Factor out the numerator and denominator)

= [2 (a + 1)(a - 1)] / [2 (a + 3) (a - 1)]

(Cancel out 2 and a-1)

= (a + 1) / (a + 3)