PreCalculus Class Notes RF8 Solving Rational Equations Algebraically and Graphically
Solving algebraically. Two equivalent methods.
x+4 1
=
+3
2x
3x
Rewrite with a common denominator
Multiply by the LCD
3 ( x + 4 ) 2 (1) 6 x ( 3)
 x+4
 1 
6x 
=
+
 = 6 x   + 6 x ( 3)
3(2x)
2 ( 3x )
6x
 2x 
 3x 
3 ( x + 4 ) 2 (1) 6 x ( 3)
=
+
6x
6x
6x
 3 ( x + 4) 
 2 (1) 
 6 x ( 3) 
6x 
 = 6x 
 + 6x 

 6x 
 6x 
 6x 
3
 x+4 2
 1 
6x 
 = 6x 
 + 6 x ( 3)
 2x 
 3x 
3 ( x + 4 ) = 2 (1) + 6 x ( 3)
3 ( x + 4 ) = 2(1) + 6 x(3)
3 ( x + 4 ) = 2 (1) + 6 x ( 3)
3 x + 12 = 2 + 18 x
10 = 15 x
10
=x
15
2
x=
3
Alternative methods for check of rational equations
Check in ORIGINAL equation
Check for undefined values
2
2
+4
x ≠ 0 so x = is OK
1
3
3
=
+3
2
2
2   3 
3
3
3.5 = 3.5
Solve graphically:
Set equal to 0 first:
x+4 1
=
+3
2x
3x
x+4 1
− −3= 0
2 x 3x
Graph y =
x+4 1
− − 3 , use Calc Zero
2 x 3x
5
4
− =3
3− x x
Solve algebraically
Solve graphically
x2
=1
x 2 − x − 20
Solve graphically
Solve algebraically
x−3
3
6
+
+ 2
=0
x
x + 2 x + 2x
Solve algebraically
Solve graphically
x2 − x − 6 x + 2
=
x 2 + x − 12 x + 4
Solve algebraically
Solve graphically