How do I form an algebraic fraction into a single fraction in its simplest form?

When starting with a fraction with 2 individual components, before any addition, subtraction or simplification can take place, the first step will be making them both having the same denominator. Once you have 2 fractions, both with the same denominator, the fractions can be combined and the numerators of both can be combined onto the same denominator. This is done by multiplying both the numerator and denominator of one of your fractions by the demoninator of the other. This does not change the value of the fraction as both are multiplied by the same value (i.e. if the multiplier used on the top and bottom of the fraction were divided their value would still be 1). Once both fractions have the same denominator, the numerator of the first fraction can be added/subtracted from the numerator of the second fraction, both on top of the same denominator. The result of this numerator then needs to be expanded out/simplified, or seperated into brackets, with potential cancelling out of common factors on both the numerator and the denominator of the fraction. This wil result in a single fraction in its simplest form.