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 x3 x 9 x3 2. 4. 2 x2 x2 x3 x6