Answer:

The simplified expression is 5/6.

Step-by-step explanation:

To simplify the expression (3a/b)^(-1) + (2b/a)^(-1), we can apply the properties of exponents.

The reciprocal of a fraction raised to a power can be obtained by taking the reciprocal of the fraction and changing the sign of the exponent.

Let's simplify step by step:

(3a/b)^(-1) + (2b/a)^(-1)

Reciprocal of (3a/b):

(1 / (3a/b))

Taking the reciprocal and changing the sign of the exponent:

(b / (3a))

Reciprocal of (2b/a):

(1 / (2b/a))

Taking the reciprocal and changing the sign of the exponent:

(a / (2b))

Now, the expression becomes:

(b / (3a)) + (a / (2b))

To add these fractions, we need a common denominator. The common denominator is 6ab.

Multiplying the first fraction by (2b/2b) and the second fraction by (3a/3a), we get:

((2b * a) / (2b * 3a)) + ((3a * b) / (3a * 2b))

Simplifying the numerators, we have:

(2ab / 6ab) + (3ab / 6ab)

Combining the fractions, we get:

(2ab + 3ab) / 6ab

Simplifying the numerator, we have:

5ab / 6ab

The common factors of ab in the numerator and denominator cancel out, leaving us with:

5 / 6

[tex]\huge {\colorbox{lavender}{Answer}}[/tex]

[tex] {m}^{ - 1} = \frac{1}{m} [/tex]

(3a / b) ^ - 1 = b/ 3a

a / 2b

a/ 2b + b / 3a =

LCM is 6ab

3a² + 2b² / 6ab