DIVIDING RATIONAL
EXPRESSION
STEP-BY-STEP SOLUTION
1. Change the division sign to multiplication sign.
2. Flip the second rational expression.
3. Factor all numerators and denominators.
4. Cancel the common factors.
5. Multiply across. Simplify if possible.
EXAMPLE NO.1
3𝑥
2
6y
𝑥
3𝑥 6y
·
2
𝑥
3𝑥 x
·
2 6𝑦
3𝑥 x
·
2 6𝑦
𝑥 x
·
2 2𝑦
𝑥²
4y
÷
EXAMPLE NO.2
3𝑥³
4
÷
9x
10
3𝑥³ 10
·
4 9𝑥
𝑥² 5
·
2 3
3𝑥³ 9x
·
4 10
3𝑥³ 10
·
4 9𝑥
5𝑥²
6
EXAMPLE NO.3
𝑎³
18
÷
a²
48
𝑎³ 48
·
18 𝑎²
𝑎
3
·
8
𝑎³ a²
·
18 48
𝑎³ 48
·
18 𝑎²
8a
3
EXAMPLE NO.4
8𝑥
3x+6
÷
12x²
5𝑥+10
8𝑥
12x²
·
3x+6 5𝑥+10
8𝑥
5x+10
·
3x+6 12𝑥²
8𝑥
5(x+2)
·
3(x+2)
12𝑥²
2 5
·
3 3𝑥
10
9x
EXAMPLE NO.5
x2 −3x−10
x−5
÷ 2
2
x −4x+4 x −2x
x2 −3x−10
x−5
· 2
2
x −4x+4 x −2x
x2 −3x−10 x2 −2𝑥
·
2
x −4x+4
𝑥−5
(𝑥+2)(𝑥−5) 𝑥(𝑥−2)
·
𝑥−2 𝑥−2
x−5
(𝑥+2)(𝑥−5) 𝑥(𝑥−2)
·
𝑥−2 𝑥−2
x−5
𝑥(𝑥 + 2)
x−2
EXAMPLE NO.6
x2 −8x+15 x2 +𝑥−20
÷ 2
2
x −x−6
𝑥 −6𝑥+8
x2 −8x+15 x2 +𝑥−20
· 2
2
x −x−6 𝑥 −6𝑥+8
x2 −8x+15 𝑥 2 −6𝑥+8
· 2
2
x −x−6 𝑥 +𝑥−20
(𝑥−5)(𝑥−3) (𝑥−2)(𝑥−4)
·
(𝑥−3)(𝑥+2) (𝑥−4)(𝑥+5)
(𝑥−5)(𝑥−3) (𝑥−2)(𝑥−4)
·
(𝑥−3)(𝑥+2) (𝑥−4)(𝑥+5)
(𝑥 − 5)(𝑥 − 2)
(𝑥 + 2)(𝑥 + 5)
ANSWER THE FOLLOWING
7𝑝
p+2
÷
p+2
𝑝
5𝑎+2
b
÷
𝑎+2
𝑏
Answer
ANSWER THE FOLLOWING
2
2𝑥
4𝑥
÷
2
𝑥
2
𝑥 −9𝑥−10
x2 +𝑥−6
÷
2
x −1
𝑥 2 −4
Answer
ANSWERS
7𝑝²
(𝑝+2)²
5
Back
ANSWERS
𝑥²
4
(𝑥−10)
(𝑥−1)
THANK YOU FOR LISTENING.