Rational expressions flashcards for Algebra review

Question 1

What is a rational expression?

Accepted Answer

A rational expression is a quotient $\frac{P(x)}{Q(x)}$ where $P(x)$ and $Q(x)$ are polynomials and $Q(x)
eq 0$.

Question 2

Add and simplify: $\frac{2}{x}+\frac{3}{x+1}$.

Accepted Answer

$$\frac{2}{x}+\frac{3}{x+1}=\frac{2(x+1)+3x}{x(x+1)}=\frac{5x+2}{x(x+1)},\quad x
eq 0,-1.$$

Question 3

Simplify the complex fraction $\frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x}-\frac{1}{y}}$.

Accepted Answer

Use the LCD $xy$ to clear denominators: $$\frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x}-\frac{1}{y}}=\frac{\frac{x+y}{xy}}{\frac{y-x}{xy}}=\frac{x+y}{y-x}.$$ (Restrictions: $x
eq 0,\ y
eq 0,\ x
eq y$.)

Rational expressions flashcards for Algebra review

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