Question

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

Answer 1

Given:

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

To find:

Simplified value of the given expression.

Solution:

1) We will solve the given algebraic expression by taking the LCM of the denominator of the expression.

2) The given term is expressed as:

• (a+b)^-1(a^-1+b^-1)

• $\frac{1}{a+b} (\frac{1}{a} +\frac{1}{b} )$

• $\frac{1}{a+b} (\frac{a + b}{ab})$

Now the term a+b will be canceled by each other.

• 1/ab

The Simplified value of the given expression is 1/ab.

Answer 2

Answer:

1/ab

Step-by-step explanation:

=(a+b)^-1.(a^-1+b^-1)

=1/(a+b) (1/a+1/b)

=1/a+b (b+a/ab) [LCM]

=(1/(a+b)) ((a+b)/ab) [(a+b) will get cut]

=1/ab