Adding & Subtracting Algebraic Fractions Flashcards

All 5 cards in this deck

What are the steps to write a sum of algebraic fractions as a single fraction?

e.g. $\frac{2}{x}+\frac{3}{x+1}$

1. Common denominator: $x(x+1)$
2. Numerator: $2(x+1)+3x$
3. Expand and collect: $\frac{5x+2}{x(x+1)}$

How do you combine an integer with an algebraic fraction into a single fraction?

e.g. $6+\frac{x-1}{x-2}$

Write the integer over the same denominator, then add the numerators.

e.g. $\frac{6(x-2)+(x-1)}{x-2}=\frac{7x-13}{x-2}$

True or false? $\frac{3}{x+1}+\frac{1}{x-2}=\frac{4}{2x-1}$

False. You cannot add numerators and denominators; you must use a common denominator, here $(x+1)(x-2)$.

True or false? When subtracting algebraic fractions, the second numerator must be put in brackets before expanding.

True. The subtraction applies to every term of that numerator, e.g. $-(x^2+5x+6)=-x^2-5x-6$.

How do you add algebraic fractions with numerical denominators?

e.g. $\frac{x}{2}+\frac{x+1}{5}$

Use the lowest common multiple of the numbers as the denominator.

e.g. $\frac{5x+2(x+1)}{10}=\frac{7x+2}{10}$