Rational expression
Simplify rational expressions in Grade 9 Algebra by factoring numerator and denominator and canceling common factors. State any restrictions on the variable.
Key Concepts
Property A rational expression is an expression with a variable in the denominator. A key rule is that the denominator cannot equal zero, so any variable value that causes this is not allowed.
Examples In the expression $\frac{5}{x}$, the restriction is $x \neq 0$. For $\frac{a+b}{c 3}$, the value $c=3$ is not allowed, so we state $c \neq 3$. In $\frac{m^2}{k(p+2)}$, we have two restrictions: $k \neq 0$ and $p \neq 2$.
Explanation Think of rational expressions as fancy fractions that have variables in them! The most important rule in their world is that you can never, ever have a zero in the denominator. It's like trying to divide a pizza among zero friends—it just doesn't make sense! So, we always point out the values that are forbidden for the variables.
Common Questions
What is a rational expression in algebra?
A rational expression is a fraction where both the numerator and denominator are polynomials. Examples include (x + 3)/(x - 2) and (x² - 1)/(x + 1). The denominator cannot equal zero.
How do you simplify a rational expression?
Factor the numerator and denominator completely, then cancel any factors that appear in both. State any excluded values—x-values that make the denominator zero—as part of the simplified result.
What are the domain restrictions of a rational expression?
The domain excludes any x-values that make the denominator equal to zero. Set each factor of the denominator to zero and solve to find all restrictions. These restrictions apply even after simplification.