Review rational expressions foundations. Math 20-1 Alberta Grade 11.
Lesson 6.1 of Rational Expressions and Equations in Math 20-1 — Alberta curriculum lessons.
1. Adding and Subtracting.
2. Multiplying.
3. Dividing — Keep, Change, Flip.
BEDMAS Reminder. When operations are mixed, follow BEDMAS: Brackets, Exponents, Division, Multiplication, Addition, Subtraction. Division and Multiplication have equal priority, so work left to right when they appear together.
Definition: Rational Expression. A rational expression is an algebraic expression that can be written as the quotient of two polynomials — essentially a fraction with variables. Examples: (5x)/(15x), (x^2 + 2x + 1)/((3x+1)(x+1)).
The Golden Rule for Reducing. Reducing a rational expression works exactly like reducing a regular fraction: cancel common factors from the numerator and denominator.
Critical rule: You can only cancel factors (things being multiplied), never terms (things being added or subtracted). In (x+2)/(x-1) you cannot cancel the x's — they are part of larger terms, not standalone factors. You must factor first.
Evaluate (9)/(5) + (2)/(7) - 3.
Part a) — (9)/(5) + (2)/(7) - 3. Step 1 — Find the LCD.
The denominators are 5, 7, and 1 (since 3 = (3)/(1)). Since 5 and 7 share no common factors, the LCD is 5 × 7 = 35.
Step 2 — Rewrite each fraction with denominator 35.
(9)/(5) = (9 × 7)/(5 × 7) = (63)/(35)
(2)/(7) = (2 × 5)/(7 × 5) = (10)/(35)
3 = (3 × 35)/(1 × 35) = (105)/(35)
Step 3 — Combine the numerators.
(63)/(35) + (10)/(35) - (105)/(35) = (63 + 10 - 105)/(35) = (-32)/(35)
Step 4 — Check if it reduces.
32 = 2^5 (only factor of 2); 35 = 5 × 7 (no factor of 2). No common factor — already in lowest terms.
Answer: -(32)/(35)
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