## Exploring the Expression (b/a-a/b)*1/b+a

This article aims to explore the mathematical expression **(b/a-a/b) 1/b+a* and delve into its simplification and understanding.

### Understanding the Expression

The expression involves basic arithmetic operations:

**Division:**b/a and a/b represent the division of b by a and a by b respectively.**Subtraction:**The expression within the parentheses involves subtracting a/b from b/a.**Multiplication:**The result of the subtraction is multiplied by 1/b.**Addition:**Finally, 'a' is added to the product.

### Simplifying the Expression

**Finding a Common Denominator:**To subtract fractions, they must have a common denominator. The common denominator for b/a and a/b is 'ab'.- b/a = (b * b)/(a * b) = b²/ab
- a/b = (a * a)/(a * b) = a²/ab

**Subtracting the Fractions:**- (b/a - a/b) = (b²/ab - a²/ab) = (b² - a²)/ab

**Multiplying by 1/b:**- [(b² - a²)/ab] * (1/b) = (b² - a²)/(ab²)

**Adding 'a':**- (b² - a²)/(ab²) + a = (b² - a² + a³b²)/(ab²)

### Final Result

The simplified form of the expression is **(b² - a² + a³b²)/(ab²)**.

### Key Considerations

**Domain:**The expression is defined for all values of 'a' and 'b' except for 'a = 0' and 'b = 0' as division by zero is undefined.**Factoring:**The numerator can be factored as a difference of squares: (b² - a²) = (b + a)(b - a)**Further Simplification:**Further simplification might be possible depending on the context or specific values of 'a' and 'b'.

By following these steps, you can simplify and understand the given expression, making it easier to work with in various mathematical contexts.