Transcript Solving Equations Containing Rational Expressions

Solving Equations Containing
Rational Expressions
Solving Equations with Rational Expressions

When the denominators contain
polynomials, you need to factor the
denominator in order to determine the least
common multiple, LCM.
Solving Equations with Rational Expressions
Example 1: Solve the following equation
3
2
x 8
  2
x  2 x x  2x
3
2
x 8
 
x2 x
x( x  2)
x 8
 3 
2
x( x  2) 
 x( x  2)    x( x  2)

x( x  2)
 x  2
x
3 x  2( x  2)  x  8
Solving Equations with Rational Expressions
3x  2x  4  x  8
5x  4  x  8
4 x  12
x3
 Check your solution in the original
equation to verify the x = 3
Solving Equations with Rational Expressions
Example 2: Nathan earns $96 in the same time
that it takes Allan to earn $72. If Nathan earns
$2/hour more than Allan, find how much each
earns per hour.
Solution:
Let n be the amount in $ that Nathan earns per hour
Let n – 2 is the amount in $ that Allan earns per hour
Solving Equations with Rational Expressions
To earn $96, Nathan must work 96 hours.
n
72 hours.
To earn $72, Allan must work
n2
Since they worked the same number of hours:
96
72

n
n2
Solving Equations with Rational Expressions
96
72

n n2
 96 
 72 
n(n  2)    n( n  2) 

 n 
n2
96(n  2)  72n
Thus, Nathan earns $8/hour
96n 192  72n and Allan earns $6/hour.
96n  72n  192
24n  192
n8
Homework

Do #7, 9 ,11, 13, 15, 21, and 22 on
pages 144 & 145 for Wednesday April
29th 