Multiplication and division of Rational Expressions Presentation for Pre-Demo

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T N C A R
M F I O S

2. At the end of the lesson, the
students will be able to:
1. multiply rational expressions;
and
2. divide rational expressions

3. Multiplication of Rational Expression
If p, q, r and s are polynomials
where q ≠ 0, s ≠ 0, then
𝒑
𝒒
.
𝒓
𝒔
=
𝒑𝒓
𝒒𝒔

4. How to Multiply Rational Expressions
Step 1. Factors each numerator and
denominator completely.
Step 2. Multiply the numerators and
denominators.
Step 3. Simplify by dividing out
common factors.

5. Example:
1.
2𝑥
𝑥2−7𝑥+12
.
𝑥2−9
6𝑥2
2.
3𝑥
3𝑦−12
.
4𝑦 −16
12𝑥2

6. Division of Rational Expressions
If p, q, r and s are polynomials
where q ≠ 0, r ≠ 0, s ≠ 0, then
𝑝
𝑞
÷
𝑟
𝑠
=
𝑝
𝑞
.
𝑠
𝑟

7. How to Divide Rational Expressions
Step 1. Rewrite the division as the product
of the first rational expression and the
reciprocal of the second.
Step 2. Factors each numerators and
denominators completely
Step 3. Multiply the numerators and
denominators together,
Step 4. Simplify by dividing out common
factors.

8. Example:
𝑥2−16
4𝑦
÷
𝑥+4
2𝑦

9. A complex fraction is a fraction
that contains a fraction in the
numerator, the denominator or
both. Also, remember a fraction
bar means division.
Example:
2𝑟+4
𝑟2−4
𝑟−2
𝑟2−4𝑟+4

11. Assessment
Quiz
Get 1 whole sheet of paper. Perform the
indicate operation of the rational
expressions.
1.
5𝑝2
𝑝2−5𝑝−36
.
𝑝2−16
10𝑝
2.
3𝑠2
𝑠2 ÷
𝑠2+4𝑠2+16
𝑠3−64

12. Assignmet
In the following items, divide the rational
expressions.
1.
2𝑎2−𝑎−21
5𝑎+20
𝑎2+7𝑎+12
𝑎2+8𝑎+16
2.
3𝑞2
𝑞2+𝑞−6
.
𝑞2−9
9𝑞
÷
𝑞2+3𝑞−10
2𝑞+6