Algebra 1 Common Core Student Edition, Grade 8-9

Think
Have you solved
a similar problem
before?
Yes. In Problem 4, you
found the quotient of
tw o rational expressions.
You simplify this complex
fraction in the same way,
but first write it as a
quotient.

A complex fraction is a fraction th at contains one or m ore fractions in its num erator,

in its denom inator, or in both. You can simplify a com plex fraction by dividing its

numerator by its denominator.

Any com plex fraction of th e form - 3 - (w here b + 0, c A 0, and d + 0) can be expressed

as ab. ‘ cd’^ d

Simplifying a Complex Fraction

1

What is the simplified form of ~x + 3?

x - 2

x + 3

x2 - 4

1 .x + 3

x — 2 x2 - 4

1x2 - 4

x - 2 x + 3

1 ( x + 2 ) ( x — 2 )

x - 2 x + 3

1 (x + 2 ) ( x ^ 2 j

]X -^ 2 x + 3

x + 2

x + 3

xz - 4

Write as a quotient.

Multiply by the reciprocal.

Factor.

Divide out the common factor x - 2.

Simplify.

G o t It? 6.W hat is th e sim plified form of q +^4

2q

2 ,7-

Lesso n Ch eck

Do you kn o w HO W?

Multiply.

1 — • —

5t t 5

Divide.

3.k^2 + k.

5fc ' 15fc2

4.^8 x -^12 x 4 - ( 4 x 2 - 9)

Simplify each complex fraction.

5.

a 2 + 2 a - 8

3 a

a ~F 4

a - 2

X2 + 6x

x + 6

Do you UNDERSTAND?

MATHEMATICAL

PRACTICES

7. Reasoning Are th e com plex fractions — an d —
   equivalent? Explain. C —c


8. C o m p a r e a n d C o n t r a s t How are multiplying rational
   expressions a n d m ultiplying num erical fractions
   similar? How are they different?


9. Reasoning Consider that | -r- ^ | Why must it
   be tru e th a t b ¥= 0 , c =h 0 , a n d d =£ 0?


10. a. Writing Explain how to multiply a rational
    expression by a polynom ial,
    b. Explain how to divide a rational expression by
    a polynomial.

c

Po w er A l g eb r a.co m Lesson 11-2 Multipjying and Djviding Rational Expressions 673