Algebra 1 Common Core Student Edition, Grade 8-9

Could you also find
the restricted values
before simplifying?
Yes. You use the original
expression to find the
restrictions on x, so you
don't need to simplify
first.

When should you
factor - 1 from an
expression?
You should factor — 1
from a - x when
factoring -1 results in a
common factor.

Simplifying a Rational Expression Containing a Trinomial

What is the simplified form ofx 2 + x3x - 6 — 6? State any excluded values.

To see if there are any

common factors, factor

the numerator and the

denominator.

3x - 6 3(x -^2 )

<2 + x - 6 (x + 3)(x - 2)

Divide out the common

factor x - 2. Simplify.

State the simplified form

w ith any restrictions on

the variable.

~ (x + 3)j(^?)

3

(x + 3)

The denominator o f the original

expression is 0 when x = - 3 or

x = 2. So t h e s im p lif ie d f o r m is

x + g , where x + - 3 and x + 2.

S& G o t It? 2. W hat is th e sim plified form of th e expression? State any excluded values.

2x - 8. a 2 - 3a + 2 _ 6z + 12 9

x 2 — 2 x — I^3 cl^ —^3

C.

2z2 + 7z + 6 d.

c — c ~ 6

C2 + 5c + 6

Y ____ o

The n u m era to r an d d en o m in ato r of j p r j are opposites. To simplify th e expression,

you can factor —1 from 3 - x to get —1(—3 + x), w hich you can rew rite as — l(x - 3).

x — 3

Then simplify _■l ( x - 3 ) ‘*, J* v

Recognizing Opposite Factors

What is the simplified form of 7x4 — - 14? State any excluded values,

4-x2 (2 ~ x){2 + x)

7x - 14 7(x - 2)

—l(x - 2)(2 + x)

~ 7(x ~ 2)

-i(x -"z y(2 + x)

x + 2

Factor the num erator and the denominator.

Factor - 1 from 2 - x.

Divide out the common factor x - 2.

Simplify.

The d en o m in ato r of th e original expression is 0 w h e n x = 2. The sim plified form is

— x 7 2, where x + 2.

G

Po w er A lg eb r a.co m Lesson 11-1 Si m p l i f y i n g Ra t i o n a l Ex p r e ssi o n s 665