Question

Simplify : (2 ⁻¹ - 3 ⁻¹)⁻¹ + (6 ⁻¹ - 8 ⁻¹)⁻¹

Answer 1

Hello Mate,

Question :  (2 ⁻¹ - 3 ⁻¹)⁻¹ + (6 ⁻¹ - 8 ⁻¹)⁻¹

Answer : 30

Explanation :

(2 ⁻¹ - 3 ⁻¹)⁻¹ + (6 ⁻¹ - 8 ⁻¹)⁻¹

= (1/2 - 1/3 )⁻¹ + (1/6 - 1/8)⁻¹

Simplify (1/2 - 1/3 ) :

✿ L.C.M of 2 and 3 :

L.C.M = 2 × 3

        = 6

1/2 - 1/3 = (3-2)/6

1/2 - 1/3 = 1/6

--------------------------------------------------------------------------

Simplify (1/6 - 1/8) :

✿ L.C.M of 6 and 8 :

 

L.C.M = 2 × 3 × 2 × 2

        = 24

1/6 - 1/8 = (4-3)/24

1/6 - 1/8 = 1/24

--------------------------------------------------------------------------

Now,

(1/2 - 1/3 )⁻¹ + (1/6 - 1/8)⁻¹

= (1/6 )⁻¹ + (1/24)⁻¹

= (6/1 )¹ + (24/1)¹

= (6¹/ 1¹ ) + (24¹/1¹)

= (6/1 ) + (24/1)

= 6/1 + 24/1

We know a/b + c/b = (a + c)/b

Here :-

a = 6

b = 1

c = 24

Applying a/b + c/b = (a + c)/b , we get :

6/1 + 24/1 = (6 + 24)/1

(6 + 24)/1 = 30/1

30/1 = 30

∴ (2 ⁻¹ - 3 ⁻¹)⁻¹ + (6 ⁻¹ - 8 ⁻¹)⁻¹  = 30