## Simplifying and Combining Expressions with Variables

In mathematics, we often encounter expressions with variables. These expressions can represent different quantities or relationships. In this article, we will explore how to simplify and combine two specific expressions: **(–4/5t + 5/3s)** and **(–3 – 7/5s + 2t)**.

### Understanding the Expressions

The first expression **(–4/5t + 5/3s)** contains two terms:

**–4/5t**: This term represents a product of –4/5 and the variable 't'.**5/3s**: This term represents a product of 5/3 and the variable 's'.

Similarly, the second expression **(–3 – 7/5s + 2t)** also has three terms:

**–3**: This is a constant term, meaning it doesn't involve any variables.**–7/5s**: This term represents a product of –7/5 and the variable 's'.**2t**: This term represents a product of 2 and the variable 't'.

### Combining Like Terms

To simplify these expressions, we can combine like terms. Like terms have the same variable and exponent.

**Step 1: Identifying Like Terms:**

In the first expression, **–4/5t** and **2t** are like terms because they both have 't' as their variable.
In the second expression, **5/3s** and **–7/5s** are like terms because they both have 's' as their variable.

**Step 2: Combining Like Terms:**

**For terms with 't':**- (–4/5t + 2t) = (–4/5 + 2)t = (6/5)t

**For terms with 's':**- (5/3s – 7/5s) = (25/15 – 21/15)s = (4/15)s

### Simplifying the Expressions

Now we can rewrite our simplified expressions:

**(–4/5t + 5/3s)**simplifies to**(6/5)t + (4/15)s****(–3 – 7/5s + 2t)**simplifies to**(6/5)t – (4/15)s – 3**

### Adding the Expressions

To add the two expressions, we can combine their simplified forms:

**[(6/5)t + (4/15)s] + [(6/5)t – (4/15)s – 3]**

Combining like terms:

**(6/5)t + (6/5)t + (4/15)s – (4/15)s – 3****(12/5)t – 3**

Therefore, the sum of the expressions **(–4/5t + 5/3s)** and **(–3 – 7/5s + 2t)** is **(12/5)t – 3**.

### Conclusion

By understanding how to identify and combine like terms, we can simplify and add expressions involving variables. This process allows us to manipulate and analyze mathematical expressions more effectively.