powerpoint presentation

2. Rational expressions play a big part in algebra and are
used in studying different concepts. But what makes a
rational expression?
In arithmetic, rational expression is the quotient or
the ratio of two numbers. In algebra, it is the quotient of
two polynomials in the form
𝑎
𝑏
where a and b are both
polynomials, and b ≠ 0.
Rational expressions are algebraic expressions whose
numerator and denominator are polynomials.

3. Examples:
4
7
𝑥2
−9
𝑥4
−4𝑥2
+4
3𝑥2
𝑦
𝑧6

4. Simplify the following fractions:
• To simplify a fraction, factor out all common factors between the
numerator and denominator.
1.
15
20
=
3 . 𝟓
4 . 𝟓
- (common factor is 5) =
𝟑
𝟒
2.
54
72
=
3 . 𝟏𝟖
4 . 𝟏𝟖
=
𝟑
𝟒

5. Notice that rational expressions are basically fractions. This
means that placing fractions in lowest terms follows the same
concept as simplifying rational expressions.
Examples:
1. Simplify
4𝑎
18𝑏
=
𝟐 . 2𝑎
𝟐 . 9𝑏
→ (common factor of the number is 2) =
𝟐𝒂
𝟗𝒃
2. Simplify
2𝑥 −2𝑦
𝑥 −𝑦
.
2𝑥 −2𝑦
𝑥 −𝑦
=
2(𝒙 −𝒚)
𝒙 − 𝒚
=
2(𝒙 −𝒚)
1(𝒙 − 𝒚)
=
2
1
= 2

6. 3. Simplify
8𝑦+4
16𝑦
.
=
4(𝑦+1)
2 . 2 . 2 . 2 . 𝑦
=
𝟒(𝑦+1)
𝟐 . 𝟐 . 2 . 2 . 𝑦
=
𝒚+𝟏
𝟒𝒚
4. Simplify
15𝑎2
𝑦
9𝑎𝑦
.
=
3 . 5 . 𝑎 . 𝑎 .𝑦
3 .3 . 𝑎 .𝑦
=
𝟑 . 5 . 𝒂 . 𝑎 . 𝒚
𝟑 . 3 . 𝒂 . 𝒚
=
𝟓𝒂
𝟑

7. 5. Simplify
𝑦+4
𝑦2
−4
.
Apply distributive property. Factor y2 – 4.
=
𝑦+4
(𝑦+4)(𝑦−4)
=
1(𝒚+𝟒)
(𝒚+𝟒)(𝑦−4)
=
𝟏
𝒚−𝟒
6. Simplify
𝑥2
−𝑥 −30
2𝑥+10
=
(𝑥+5)(𝑥 −6)
2(𝑥+5)
=
(𝒙+𝟓)(𝑥 −6)
2(𝒙+𝟓)
=
𝒙 −𝟔
𝟐