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# 9 6solvingrationalexpressions-110330091103-phpapp01

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### 9 6solvingrationalexpressions-110330091103-phpapp01

1. 1. 9.69.6 Solving Rational EquationsSolving Rational Equations p.505p.505
2. 2. Hint for solving:Hint for solving: • A quick way to solve a rationalA quick way to solve a rational equation is to multiply everythingequation is to multiply everything through by the LCD.through by the LCD. • This will get rid of all the fractions!This will get rid of all the fractions! • Beware of extraneous solutions!Beware of extraneous solutions!
3. 3. Example: Solve. xx 12 2 13 =− LCD: 2x Multiply each fraction through by the LCD x xx x x 12*2 2 23*2 =− 246 =− x 18=− x 18−=x Check your solution!Check your solution! 18 12 2 1 18 3 − =− − 1293 =+
4. 4. Solve. 1 5 4 1 5 + −= + xx x LCD: ? LCD: (x+1) )1( )1(5 )1(4 )1( )1(5 + + −+= + + x x x x xx 5445 −+= xx 145 −= xx 1−=x Check your solution!Check your solution! 11 5 4 11 )1(5 +− −= +− − 0 5 4 0 5 −= − ? No Solution!No Solution!
5. 5. Solve. 1 4 6 2 23 2 + − = − − xx x Factor 1st ! 1 )2)(2( 6 2 23 + −+ = − − xxx x LCD: (x+2)(x-2) )2)(2( )2)(2( )2)(2(6 )2( )2)(2)(23( −++ −+ −+ = − −+− xx xx xx x xxx 42264263 22 −+−+=−−+ xxxxxx 2443 22 +=−+ xxx 0642 2 =−+ xx 0322 =−+ xx 0)1)(3( =−+ xx 01or03 =−=+ xx 1or3 =−= xx Check your solutions!Check your solutions!
6. 6. Short Cut! When there is only fraction on each sideWhen there is only fraction on each side of the =, just cross multiply as if youof the =, just cross multiply as if you are solving a proportion.are solving a proportion.
7. 7. Example: Solve. 4 1 4 3 2 + = + xxx xx 42 + 12342 +=+ xxx 0122 =−+ xx 0)3)(4( =−+ xx 03or04 =−=+ xx 3or4 =−= xx Check your solutions!Check your solutions! )4(3 += x
8. 8. One more SAT Question 43)( 1642)( 2 2 −−= −−= xxxg xxxf If Which of the following is an expression for ? )( )( xg xf 1 42 . 1 42 . 4 3 4 . 12. 3 22 . 2 2 − − + + ++ −− x x e x x d xxc xxb a
9. 9. Now you try!Now you try! Pg 509 #’s 6-9 allPg 509 #’s 6-9 all