Algebra 1 Common Core Student Edition, Grade 8-9

a 1 + 3 - 2 b ± + 1 = 1.

a- 3 + x “ x d,Vx + 3 3x

^ Go t It? 1. W hat is the solution of each equation? C heck your solution.

To solve som e rational equations, you n e e d to factor a q uadratic expression.

Think
Is there a different
way to solve this
equation?
Yes. Because it's a
quadratic equation, you
can also solve it by using
the quadratic formula, by
completing the square, or
by graphing.

Problem 2 So l v i n g b y Fact o r i n g^

Multiple Choice What are the solutions of 1 - | = ^§?

CA) -11,12 -4,3 C D -3,4 CD 12, 13

The denominators are x and x 2 .The LCD is x 2.

x2( 1 - - J = x 2 ( 1| ) M ultiply each side by x 2.

x 2 (l) - Xx 2 [ j ~ ) ~ ^ ( ^ r ) Distributive Property

x - x = 12

x 2 - x - 12 = 0

(x - 4)(jc + 3) = 0

x-4 = 0or x + 3 = 0

x = 4 or x = —3

Simplify.

Collect terms on one side.

Factor the quadratic expression.

Zero-Product Property

Solve fo r x.

Ch e c k D eterm ine w h e th e r 4 an d - 3 b o th m ake 1 - ^ H a tru e statem ent.

W hen x = 4:

iJ- - I = I?.o

1 -^1 2 _^12

4 (4 )2

W hen x = —3:

1 _ 1 _ 12

x x 2

1? 12

(~ 3 ) ( - 3 ) 2

1 +U I 2

1 3 9

4 4

The solutions are 4 a n d - 3. The correct answ er is C.

* G o t It? 2. W hat are th e solutions of each eq u a tio n in p arts (a) a n d (b)?

Check your solutions.

, 5 - a. - = -= (^6) ■ c — 6
y y2
b. d + 6 =d+d + 3^11
c. R e a s o n in g How can you tell th a t th e rational eq u a tio n -5 = — 1
has no solutions just by looking at th e equation?
692 C h a p te r 11 Rat io nal Expressions and Funct ions