Question

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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 :

$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 2 , 3 } \\ \cline{1-2} \tt 3 & \sf { 1 , 3 } \\ \cline{1-2} \tt & \sf{ 1 , 1 }\end{array}}$

L.C.M = 2 × 3

          = 6

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

1/2 - 1/3 = 1/6

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Simplify (1/6 - 1/8) :

✿ L.C.M of 6 and 8 :

$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 6 , 8 } \\ \cline{1-2} \tt 3 & \sf { 3 , 4 } \\ \cline{1-2} \tt 2 & \sf{ 1 , 4 } \\ \cline{1-2} \tt 2 & \sf{ 1 , 2 } \\ \cline{1-2} \tt & \sf{1, 1}\end{array}}$

L.C.M = 2 × 3 × 2 × 2

          = 24

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

1/6 - 1/8 = 1/24

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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

Answer 2

Given to simplify:-

${( {2}^{ - 1} - {3}^{ - 1} )}^{ - 1} + {( {6}^{ - 1} - {8}^{ - 1} )}^{ - 1}$

Solution:-

${( {2}^{ - 1} - {3}^{ - 1} )}^{ - 1} + {( {6}^{ - 1} - {8}^{ - 1} )}^{ - 1}$

$= {( \frac{1}{2} - \frac{1}{3} )}^{ - 1} + {( \frac{1}{6} - \frac{1}{8} )}^{ -1 }$

$= {( \frac{3 - 2}{6}) }^{ - 1} + {( \frac{4 - 3}{24}) }^{ - 1}$

$= {( \frac{1}{6}) }^{ - 1} + {( \frac{1}{24}) }^{ - 1}$

$= 6 + 24$

$= 30$

Answer:-

• Answer is 30.