Algebra 1 Common Core Student Edition, Grade 8-9

Plan
Why write the
polynomial as a
rational expression?
To divide a rational
expression by a
polynomial, you have to
multiply by the reciprocal
of the polynomial.
Writing the polynomial
over 1 may help you find
its reciprocal.

1*2 9 ^ y — ^

What is the quotient ^ + w ^ + Sx + i 4?

Dividing Rat ional Expressions

j

To divide by a rational expression, x 2 - 25 x - 5

multiply by its reciprocal. 4 x + 2 8 ' x2 + 9x + 14

x 2 -2 5 x 2 + 9x + 14

4x + 28 x - 5

Before multiplying, factor. _ ( x + 5 ) ( x - 5 ) ( x + 7 ) ( x + 2 )

4(x + 7) ’ x - 5

Divide out the common factors _ ( x + 5) ( x— ^ (x—K7}1(x + 2)

x-5andx + 7. 4j(x—KT) iX-—“" S

Multiply numerators and ( x + 5 )(x + 2)

multiply denominators. Leave the = 4

quotient in factored form.

€

G o t It? 4. W hat is th e quotient?

_________________________________________________x xy. 4f c + 8. fc2 + 6f c + 8

x + y ' x + y 6 fc-10’ 9fc - 15

The reciprocal of a polynom ial such as x + 3x + 2 is 2 JC — 1

Problem 5

Multiple Choice What is the quotient ~u - 5r 12x + (x2 — 3x — 4)?

Dividing a Rational Expression by a Polynomial

• ]
  5x
  3x 3x 3(x - 4)2(x + 1)
  CA> 77— rvTTTT ( x - 4 ) ( x + 1) C D — 5 x 2 + 5 7 TTTT C O 5 x 5 ( x + 1)

1

5x 1 5x x2 — 3x — 4

3x(x — 4) 1

M ultiply by the reciprocal.

5x (x — 4)(x + 1) Factor.

3x](x -<4jl__ 1 ______ Divide out the common

5^ ’ jfx-^Tjfx + 1 ) factors x and x - 4.

3

5(x + 1)

The correct answ er is D.

G o t It? 5. W hat is th e q u o tien t -- * 1 + ( z — 1)?

Simplify.

672 C h a p t e r 11 Rat i o n al Exp r essi o n s an d Fu n ct i o n s