Algebra 2—Chapter 9: Solving Rational Equations Notes
Step 1: Determine what value x cannot be in a cloud. (Set all denominators equal to zero and solve)
Step 2: Find the LCM (Remember to factor denominators!!)
Step 3: “Zap” each term with the LCM. Cancel where appropriate, distribute as needed
Step 4: Solve for x. You might have to factor or use the Quadratic Formula….
Step 5: Check to be sure that x does not equal any number from Step 1.
If you multiply every term by the LCD, it gets rid of all fractions. Then you can solve the resulting equation.
Ex:
3
5
8x
 
 x cannot be -2
x  2 4 4x  8
3
5
8x
 
 LCD is 4(x + 2)  multiply this times every term
x  2 4 4( x  2)
3(4)
5( x  2)
8x


( x  2)4 4( x  2) 4( x  2)
12  5( x  2)  8 x  after you multiply by the LCD, fractions are gone!
12  5x  10  8x  solve this new equation
22  3x 
x
1.
9
2
2


10 x  1 5
3.
12 x  19
3
5


x  7 x  12 x  3 x  4
2
22
3
and since it’s not -2 then 22/3 is okay!
1
5
2
 2

x3 x 9 x3
2.
4. 2 
x2 x2

x3 x6