Algebra 1 Common Core Student Edition, Grade 8-9

Some rational equations are proportions. You can solve th e m by using th e Cross

Products Property.

Think- _

Can you use the

LCD to solve this

equation?

Yes, but when each side

of a rational equation

is a single rational

expression, using cross

products is often easier.

Otherwise, you have to

multiply each side of the

equation by the LCD,

(x + 2 )(x + 1 ).

Ih jp iS L ^
What extraneous
solutions are
possible?
Since+5 and
are undefined when
x = - 5 , a possible
extraneous solution
is - 5.

694 C h a p t e r 11

Problem 4I S o l v i n g a R a t i o n a l P r o p o r t i o n

What is the solution of

x + 2 x + 1

4 ( x + 1) = 3 ( x + 2 ) Cross Products Property

4x + 4 = 3x + 6 Distributive Property

x = 2 Solve fo r x.

Check 2+ 2 4? 2+ 1 3

1 = 1

G o t It? 4. Find the solution(s) of each equation. C heck your solutions.

_ 3 _ 5 h c _ 7

b + 2 b - 2 3 c — 4

The process of solving a rational eq u a tio n m ay give a solution th a t is extraneous

because it m akes a d en o m in ato r in th e original eq u a tio n equal 0. An extraneous

solution is a solution of an e quation th a t is derived from th e original equation, b u t is

no t a solution of th e original equation itself. So you m u st check your solutions.

Checking to Find an Extraneous Solution

What is the solution of x + 5 = J+""§?

6 x + 3

x + 5 x + 5

6 ( x + 5 ) = ( x + 3 ) ( x + 5 ) Cross Products Property

6 x + 30 = x 2 + 8 x + 15 Simplify each side o f the equation.

0 = x 2 + 2 x - 15 Collect terms on one side.

0 = ( x - 3 ) ( x + 5 ) Factor.

x-3 = 0orx + 5 = 0 Zero-Product Property

x = 3 o r x = —5 Solve fo r x.

Check^6? 3 + 3^6? -5 + 3

3+5 3+5 -5+5 -5+5

! =! § = 1T * Undefined!

The equation has one solution, 3.

G o t It? 5. W hat is th e solution of \ 4 = x _22? C heck your solution.

Rat io nal Expressions and Funct ions