Algebra is an important branch of mathematics that **involves using letters, numbers, and symbols to represent and manipulate mathematical expressions and equations. **In GCSE Mathematics, algebraic concepts and techniques play a major role in solving various problems.

Let's start by considering a **simple example:**

**find the value of a number 5 more than twice another number.**

Let's call the unknown **number "x"** and the **other number "y".** Using algebra, we can write this as:

**x = 2y + 5**

Here, the letter **"x"** represents the number we want to find, **"y"** represents the other number, and **the expression "2y + 5" represents the condition that the first number is 5, more than twice the second number.**

Once we have set up the equation, we can **use algebraic techniques to solve for "x".** For example, we can **rearrange the equation **to get "y" in terms of "x":

y = \(\frac{(x-5)}{2}\)

**Now,** we can **substitute any value of "x"** into this expression to find the corresponding value of "y".

Another **important concept in algebra is factorisation.** This **involves breaking down a mathematical expression into simpler terms that can be more easily manipulated or solved.** For example, consider the quadratic equation:

x^{2} + 5x + 6 = 0

We can **factorise this equation as:**

(x + 2)(x + 3) = 0

This tells us that **the solutions to the equation** are **x = -2 and x = -3.**

Algebraic fractions can also be challenging for some students. However, with practice, they can become easier to handle. **For example, consider the fraction:**

\(\frac{(2x + 3)}{(x - 4)}\)

We can simplify this fraction by factorising the numerator:

**\(\frac{(2x + 3)}{(x - 4)}\) = \(\frac{(2x + 3)}{(x - 1)-3}\)**

**= \(\frac{(2x + 3)}{(x - 1)-3}\) - \(\frac{(2x + 3)}{3}\)**

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