Question

(a^-1+b^-1)*(a+b)^-1

Answer 1

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Answer 2

To simplify the given expression, we can follow these steps:

Step 1: Find the inverse of each term. Step 2: Add the inverses. Step 3: Take the inverse of the sum.

Let's proceed with the steps:

Step 1: Find the inverse of each term The inverse of a number 'x' is denoted as 'x^-1' and is defined as 1/x.

Inverse of 'a': a^-1 = 1/a Inverse of 'b': b^-1 = 1/b

Step 2: Add the inverses (a^-1 + b^-1) = (1/a + 1/b)

Step 3: Take the inverse of the sum To take the inverse of the sum, we invert the result obtained from Step 2:

[(1/a) + (1/b)]^-1

Now, to simplify this expression further, we need to find a common denominator and combine the fractions:

Common denominator: 'ab'

[(b + a) / (ab)]^-1

Now, take the inverse:

= (ab) / (b + a)

So, the simplified expression is:

(a^-1 + b^-1)*(a + b)^-1 = (ab) / (a + b)