Example Card: Subtracting and Simplifying Rational Expressions
Simplify rational expressions in Grade 9 Algebra by factoring numerator and denominator and canceling common factors. State any restrictions on the variable.
Key Concepts
Subtraction can be tricky, but watch how simplifying at the end makes this problem elegant. This example demonstrates this key idea of subtracting rational expressions, including simplification.
Example Problem: Subtract the expressions $\frac{x+1}{2x 10} \frac{x+13}{6x 30}$.
Step by Step: 1. Begin by factoring each denominator to find their components. $$ \frac{x+1}{2(x 5)} \frac{x+13}{6(x 5)} $$ 2. Identify the least common denominator (LCD). Here, the LCD is $6(x 5)$. 3. Rewrite the first fraction as an equivalent fraction with the LCD. The second fraction already has the LCD's factors. $$ \frac{3(x+1)}{6(x 5)} \frac{x+13}{6(x 5)} $$ 4. Combine the fractions by subtracting the numerators. Be careful to distribute the negative sign. $$ \frac{3(x+1) (x+13)}{6(x 5)} $$ 5. Expand the expression in the numerator and collect like terms. $$ \frac{3x + 3 x 13}{6(x 5)} = \frac{2x 10}{6(x 5)} $$ 6. Factor the numerator to check for common factors with the denominator. $$ \frac{2(x 5)}{6(x 5)} $$ 7. Divide out the common factor $(x 5)$ to simplify the expression. $$ \frac{2}{6} = \frac{1}{3} $$.
Common Questions
What is Example Card: Subtracting and Simplifying Rational Expressions in Grade 9 Algebra?
Subtraction can be tricky, but watch how simplifying at the end makes this problem elegant Mastering this concept builds a foundation for advanced algebra topics.
How do you approach Example Card: Subtracting and Simplifying Rational Expressions problems step by step?
This example demonstrates this key idea of subtracting rational expressions, including simplification Use this method consistently to avoid common errors.
What is a common mistake when studying Example Card: Subtracting and Simplifying Rational Expressions?
Begin by factoring each denominator to find their components Always check your work by substituting back into the original problem.