Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Solving
Rational Equations
By: Ms. Ruth Good
Algebra 2
Rational Equations
• Def: Equations with a variable in
the denominator
• Example:
1
2
1
=
+
+
x
x
x
Steps for Solving:
Find LCD of all terms in equation.
Multiply both sides of equation by
LCD.
(This results in a new equ...
Definition
• Some answers will
not work in the
original equation
because they will
make the
denominator equal
zero. These ...
Example 1: Solve
Find LCD. LCD = 2x
xx
12
2
13
=−
x
xx
x 2
12
2
13
2 





=





− Multiply both sides by 2x....
Checking Ex. 1:
Substitute in x = -18.
18
12
2
1
18
3
−
=−
−
Get common denominators.
18
12
18
12
18
12
18
9
18
3
−
=
−
−
...
Example 2: Solve
LCD = x + 1
1
5
4
1
5
+
−=
+ xx
x
( ) ( )1
1
5
4
1
5
1 +





+
−=





+
+ x
xx
x
x
5445 −+=...
Example 3: Solve
Factor denominator of second fraction.1
4
6
2
23
2
+
−
=
−
−
xx
x
1
)2)(2(
6
2
23
+
−+
=
−
−
xxx
x
LCD = ...
Example 4: Solve
4
1
4
3
2
+
=
+ xxx
What is different about this equation?
3x + 12 = x2
+ 4x Cross-Multiply
0 = x2
+ x – ...
Example 4: Solve
4
1
4
3
2
+
=
+ xxx
What is different about this equation?
3x + 12 = x2
+ 4x Cross-Multiply
0 = x2
+ x – ...
Upcoming SlideShare
Loading in …5
×

Rational equations

3,948 views

Published on

How to Solve Rational Equations

Published in: Education
  • Sex in your area is here: ♥♥♥ http://bit.ly/2ZDZFYj ♥♥♥
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • Follow the link, new dating source: ♥♥♥ http://bit.ly/2ZDZFYj ♥♥♥
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here

Rational equations

  1. 1. Solving Rational Equations By: Ms. Ruth Good Algebra 2
  2. 2. Rational Equations • Def: Equations with a variable in the denominator • Example: 1 2 1 = + + x x x
  3. 3. Steps for Solving: Find LCD of all terms in equation. Multiply both sides of equation by LCD. (This results in a new equation which may not equal the original equation.) Solve resulting equation. Check answers in original equation.
  4. 4. Definition • Some answers will not work in the original equation because they will make the denominator equal zero. These are called extraneous roots.
  5. 5. Example 1: Solve Find LCD. LCD = 2x xx 12 2 13 =− x xx x 2 12 2 13 2       =      − Multiply both sides by 2x. 246 =− x Solve. 18 18 −= =− x x Now we must check…
  6. 6. Checking Ex. 1: Substitute in x = -18. 18 12 2 1 18 3 − =− − Get common denominators. 18 12 18 12 18 12 18 9 18 3 − = − − =− − It checks!!! X = -18
  7. 7. Example 2: Solve LCD = x + 1 1 5 4 1 5 + −= + xx x ( ) ( )1 1 5 4 1 5 1 +      + −=      + + x xx x x 5445 −+= xx 1−=x Solve. 0 5 4 0 5 −= − Doesn’t check. No Solution!! Check:
  8. 8. Example 3: Solve Factor denominator of second fraction.1 4 6 2 23 2 + − = − − xx x 1 )2)(2( 6 2 23 + −+ = − − xxx x LCD = (x+2)(x-2) )2)(2(1 )2)(2( 6 2 23 )2)(2( −+      + −+ =      − − −+ xx xxx x xx ( )( ) )2)(2(6223 +−+=+− xxxx 1,3 0)1)(3(2 0)32(2 0642 464263 2 2 22 −= =−+ =−+ =−+ −+=−−+ x xx xx xx xxxx Solve. We still need to check. X = -3, 1
  9. 9. Example 4: Solve 4 1 4 3 2 + = + xxx What is different about this equation? 3x + 12 = x2 + 4x Cross-Multiply 0 = x2 + x – 12 Solve 0 = (x + 4)(x – 3) x = -4, 3 Check X = 3
  10. 10. Example 4: Solve 4 1 4 3 2 + = + xxx What is different about this equation? 3x + 12 = x2 + 4x Cross-Multiply 0 = x2 + x – 12 Solve 0 = (x + 4)(x – 3) x = -4, 3 Check X = 3

×