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Starting off with ‘Syms Matlab Combine into One Fraction’, let’s understand the context. The software Matlab is essential in various aspects of mathematics, it’s used for numeric computation, visualization and programming. ‘Syms’ is a function in Matlab that helps to carry out symbolic computations. This can be really effective when one needs to do tasks like simplifying a symbolic expression, expand or combine them. Today, we’ll explore how we can easily combine fractions into one using syms in Matlab.

First, let’s start with the solution to the problem. To combine fractions in Matlab using syms, you would use the `sym` function to define your variables as symbolic. Then, you can use the `collect` function to combine the fractions.

syms x f = 1/x + 1/x^2; f_combined = collect(f);

In the above code, `syms x` is used to create a symbolic variable x. Then, the example fraction `1/x + 1/x^2` is defined. The `collect` function will then combine f into one fraction.

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## Syms Function in Matlab

Matlab’s symbolic math toolbox contains various kinds of functions like **syms**, which is used for symbolic computations. Symbolic variables are different from regular Matlab variables in that they allow exact computations, which comes in handy when you’re dealing with mathematical formulas.

## Collect Function in Matlab

On the other hand, `collect` combines the fractions. As stated earlier, symbolic computing allows for mathematical manipulations to be performed in an algebraic manner. So when `collect` is called, it will express the equation as a polynomial in specified variable. For instance, `collect(f)` will take an input `f` which is an equation (like 1/x + 1/x^2), and output the equation combined into one fraction.

## Examples and Explanation

Let’s look at some examples to further understand the whole process. Consider you’ve two fractions ‘1/(x+2) + 3/(x+2)’. Using the syms and collect functions, we’ll combine them into one fraction:

syms x f = 1/(x+2) + 3/(x+2); f_combined = collect(expand(f));

**Note:** We use `expand` here before `collect` to expand out products in the expression first. The `expand` function simplifies the expression by expanding multiplications and powers, the result of `expand(f)` would simplify the expression which then can be easily combined using `collect`.

To conclude, symbolic computation is a powerful feature in Matlab which plays a significant role in managing complex mathematical tasks. The combination of various functions like `syms`, `collect` and `expand` makes it much easier. It gives accurate results, saves a considerable amount of time, and is effective-especially for tasks like combining fractions.

## Understanding Matlab Libraries

Matlab includes a vast number of libraries and toolboxes which are ultimate collections of Matlab functions (M-files) that extends the Matlab environment to solve particular classes of problems. These toolboxes are used in a wide range of applications, including maths, graphics, design modelling and many more.

## Optimizing Problem Solving with Functions

Understanding and appropriately using different Matlab functions can drastically streamline your problem-solving process. Here, in the case of combining fractions, syms and collect function did the trick. Similarly, hundreds of such functions exist in Matlab, all designed to help solve different problems efficiently. In this context, recognizing the requirements of the problem and learning to map it with the appropriate function is a pace-changing skill you can develop.

This lays out the entire process of how to combine fractions into one using syms in Matlab, including an explanation of the role of symbolic computations in this process, and the collective roles of the syms and collect functions.