2.7 solving rational equations
DESCRIPTION
2.7 Solving Rational Equations. p.228. Hint for solving:. A quick way to solve a rational equation is to multiply everything through by the LCD. This will get rid of all the fractions! Beware of extraneous solutions!. Example : Solve. LCD : 2x Multiply each fraction through by the LCD. - PowerPoint PPT PresentationTRANSCRIPT
2.7 Solving Rational Equations
p.228
Hint for solving:
• A quick way to solve a rational equation is to multiply everything through by the LCD.
• This will get rid of all the fractions!
• Beware of extraneous solutions!
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
18xCheck your solution!
18
12
2
1
18
3
1293
Solve.1
54
1
5
xx
x LCD: ?LCD: (x+1)
)1(
)1(5)1(4
)1(
)1(5
x
xx
x
xx
5445 xx
145 xx
1x
Check your solution!
11
54
11
)1(5
0
54
0
5
?
No Solution!
Solve. 14
6
2
232
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 xx0322 xx
0)1)(3( xx
01or 03 xx
1or 3 xx
Check your solutions!
Short Cut!
When there is only fraction on each side of the =, just cross multiply as if you are solving a proportion.
Example: Solve.
4
1
4
32
xxx
xx 42 12342 xxx
0122 xx0)3)(4( xx
03or 04 xx3or 4 xx
Check your solutions!
)4(3 x
Last Example: Solve. 1
2
22
62
x
x
xx
)1(6 x)2)(1(2 xxx
6)2(2 xx3)2( xx
0322 xx0)1)(3( xx
01or 03 xx1or 3 xx
1
2
)1(2
6
x
x
xx
Check your solutions!
Assignment