02Efractions-add

= Algebraic Fractions - Adding = toc

Note : When dealing with algebraic fractions, the line in the fraction that separates numerator from denominator must absolutely __always__ be horizontal. Never, ever write anything that looks like : **//3x/4//**

Literacy
In any fraction,
 * the **numerator** is the value on the top of the fraction
 * the **denominator** is the value on the bottom of the fraction.

Note : The fraction line (that is always horizontal) is called the** vinculum **. {but you don't need to remember that}

Adding Fractions
Fractions with pronumerals in them should be dealt with in the same way as normal fractions.
 * 1) Find the lowest common denominator (LCD) (often by multiplying the denominators together)
 * 2) Change each fraction so they both have the LCD
 * 3) Add (or subtract) the two numerators, keep the denominator the same.
 * 4) Simplify the numerator.

** Example 1 **
math \textbf{(a)} \quad \text{Simplify : } \dfrac{3x}{4} + \dfrac{5x}{6} math

{LCD is 12 → both 4 and 6 are factors of 12}



Note : When algebra is involved, the number part of the fraction should always be left as an improper fraction, never changed to a mixed number.

math \textbf{(b)} \quad \text{Simplify : } \dfrac{a+4}{5} - \dfrac{a-1}{2} math

{LCD is 10 → both 5 and 2 are factors of 10}

Warning : Notice that the __entire__ numerator of the second fraction is being subtracted.

** Example 2 **
math \textbf{(a)} \quad \text{Simplify : } \dfrac{3}{4x} + \dfrac{3x}{5} math

{LCD is 20x → both 4x and 5 are factors of 20x}



math \textbf{(b)} \quad \text{Simplify : } \dfrac{x-1}{x+2} - \dfrac{3}{x+3} math

{LCD is (x+2)(x+3) }



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