9.6 9.6 Solving Rational EquationsSolving Rational Equations

p.505p.505

Hint for solving:Hint for solving:

• A quick way to solve a rational A quick way to solve a rational equation is to multiply everything equation is to multiply everything through by the LCD. through by the LCD.

• This will get rid of all the fractions!This will get rid of all the fractions!

• Beware of extraneous solutions!Beware of extraneous solutions!

Example: Solve.

xx

12

2

13

LCD: 2x

Multiply each fraction through by the LCD

x

xx

x

x 12*2

2

23*2

246 x

18 x

18xCheck your solution!Check your solution!

18

12

2

1

18

3

1293

Solve.1

54

1

5

xx

x LCD: ?LCD: (x+1)

)1(

)1(5)1(4

)1(

)1(5

x

xx

x

xx

5445 xx

145 xx

1x

Check your solution!Check your solution!

11

54

11

)1(5

0

54

0

5

?

No Solution!No Solution!

Solve. 14

6

2

232

xx

x

Factor 1st!

1)2)(2(

6

2

23

xxx

x

LCD: (x+2)(x-2)

)2)(2()2)(2(

)2)(2(6

)2(

)2)(2)(23(

xx

xx

xx

x

xxx

42264263 22 xxxxxx

2443 22 xxx

0642 2 xx0322 xx

0)1)(3( xx

01or 03 xx

1or 3 xx

Check your solutions!Check your solutions!

Short Cut!

When there is only fraction on each side When there is only fraction on each side of the =, just cross multiply as if you of the =, just cross multiply as if you are solving a proportion.are solving a proportion.

Example: Solve.

4

1

4

32

xxx

xx 42 12342 xxx

0122 xx0)3)(4( xx

03or 04 xx3or 4 xx

Check your solutions!Check your solutions!

)4(3 x

One more SAT Question

43)(

1642)(2

2

xxxg

xxxfIf

Which of the following is an expression for ?)(

)(

xg

xf

1

42.

1

42.

43

4.

12.

3

22.

2

2

x

xe

x

xd

xxc

xxb

a

Now you try!Now you try!Pg 509 #’s 6-9 allPg 509 #’s 6-9 all