Simplifying Algebraic Fractions Flashcards

All 6 cards in this deck

What is the first step in simplifying an algebraic fraction?

e.g. $\frac{x^2-x-6}{2x^2-5x-3}$

Factorise the numerator and the denominator fully.

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

When are you allowed to cancel something from an algebraic fraction?

Only when it is a factor of the whole numerator and the whole denominator.

What are the steps to simplify an algebraic fraction?

e.g. $\frac{x^2-9}{x^2+3x}$

1. Factorise the numerator: $(x-3)(x+3)$
2. Factorise the denominator: $x(x+3)$
3. Cancel the common factor $(x+3)$: $\frac{x-3}{x}$

True or false? $\frac{x+2}{x}$ simplifies to $2$.

False. $x$ is not a factor of the whole numerator, so it cannot be cancelled.

True or false? $\frac{x^2-16}{x-4}$ simplifies to $x+4$.

True. $x^2-16=(x-4)(x+4)$, so the factor $(x-4)$ cancels.

How do you simplify a fraction of powers of the same letters?

e.g. $\frac{c^3d^4}{cd}$

Subtract the indices for each letter.

e.g. $c^{3-1}d^{4-1}=c^2d^3$