ALGEBRA – LESSON 93Quotient of Rational Expressions

Be ready to grade the homework!

Quotient of Rational Expressions

We know that whenever we are multiplying fractions, we can cancel like terms from the top

and bottom to simplify the equation before calculating the final answer. We will do the same thing with rational expressions with equations on

the top and bottom.

2 35 8

. 2x 76 x

. (x+1) 3 6 (x+1)

.

Quotient of Rational Expressions

1) Factor all expressions.

a) Pull out common terms.b) “Unfoil”c) Difference of 2 squares.

2) Flip and Cancel all like terms or “bricks”.

3) Multiply

Remember: Division problems become multiplication problems by flipping the 2nd fraction.

Quotient of Rational Expressions

#1

g2 + 8g + 16g2 + 9g + 20

g2 - 16g2 + 2g - 15

(g + 4)(g + 4)

(g + 4)(g + 5)

(g + 4)(g - 4)

(g + 5)(g - 3)

(g + 4)(g + 4)

(g + 4)(g + 5)x

(g + 4)(g - 4)

(g + 5)(g - 3)=

(g - 4)

(g - 3)

Quotient of Rational Expressions

#2

x2 – x – 12 x2 + 3x

x2 – 13x + 36x3 – 4x2 – 45x

(x - 4)(x + 3)

x(x + 3)

(x - 9)(x - 4)

x(x + 5)(x - 9)

(x - 4)(x + 3)

x(x + 3)x

(x - 9)(x - 4)

x(x + 5)(x - 9)= (x + 5)

Quotient of Rational Expressions

#3

p2 – p – 2 p2 + 7p + 6

p2 – 4p2 + 7p + 6

(p - 2)(p + 1)

(p + 6)(p + 1)

(p - 2)(p + 2)

(p + 6)(p + 1)

(p - 2)(p + 1)

(p + 6)(p + 1)x

(p - 2)(p + 2)

(p + 6)(p + 1)=

(p + 2)

(p + 1)

Quotient of Rational Expressions

#4

m2 – 10m + 24

m2 + 3m – 28

m2 – 36m2 + 4m - 21

(m - 6)(m - 4)

(m - 4)(m + 7)

(m - 6)(m + 6)

(m + 7)(m - 3)

(m - 6)(m - 4)

(m - 4)(m + 7)x

(m - 6)(m + 6)

(m + 7)(m - 3)=

(m + 6)

(m - 3)

Homework: Problem Set 93