Question

Find the value (7¯¹_8¯¹)¯¹_(3¯¹-4¯¹)¯¹

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Answer 1

=(1/7 - 1/8)^-1 - (1/3-1/4)^-1

= (8-7/56)^-1 - (4-3/12)^-1

=(1/56)^-1 - (1/12)^-1

=56-12

=44

Answer 2

Concept:

To solve  this question, we require the following concepts:

• Inverse of a number is the reverse of it i.e., reciprocal of that number . ($x^{-1}=\frac{1}{x}$)
• L.C.M. refers to the least common multiple of  two numbers is the smallest positive integer that is divisible by both the numbers.
• The difference of two numbers is the result of subtraction of one from other.

Given:

The expression:

(7¯¹-8¯¹)¯¹-(3¯¹-4¯¹)¯¹

To find:

The result obtained on solving the given expression.

Solution:

The  given expression can be written as:

       $(\frac{1}{7} -\frac{1}{8} )^{-1}-(\frac{1}{3} -\frac{1}{4} )^{-1}$

On taking L.c.m of the terms inside bracket.

  =   $(\frac{8-7}{56} )^{-1}-(\frac{4-3}{12} )^{-1}$

  =   $(\frac{1}{56} )^{-1}-(\frac{1}{12} )^{-1}$

  =   56 - 12

  =   44

Hence, the result of the expression is 44.