Question

pls solve it and explain wherein did 4 go ​

Answer 1

Note :

To get the reciprocal (multiplecative inverse) of a rational number, interchange its numerator and denominator.

Analytical definition of multiplecative inverse:

Multiplecative inverse of a number is the number, which when multiplied by the given number, given the result 1.

If it is given that;

a•b = 1

=> a = 1/b

or

=> b = 1/a

Here,

a is the multiplecative inverse of b and b is the multiplecative inverse of a.

Here,

The given expression is ;

=> (a+2) + 4/(a-2)

=> { (a+2)(a-2) + 4 }/(a-2)

=> { (a^2 - 2^2 ) + 4 }/(a-2)

=> { a^2 - 4 + 4 }/(a-2)

=> a^2/(a-2)

Thus ,

To get its multiplecative inverse of the given expression, interchange the numerator and the denominator.

Hence,

The multiplecative inverse of the given expression is :

(a-2)/a^2

Hence,

The appropriate answer is :

option (c).