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Unformatted text preview: Mat120 Chapter 11  Section 6 Page 2‘! SQLVlNG RATlCiNAL {QUAUONS _
1.’ LiSt restrictiuns’ on thevariable. Amid any values of the variable that make a I denominator zero. _ 2. Clear the equation of fractions by multiplying both sides by the LCD of all
rational expressions in the equation. ‘
3. Solve the resulting equation. 4. Reject any proposed solution that is in the list of restrictions on the variable.
Check other proposed solutions in the on‘ginal equation. Solving a Rational Equation Solve: x + ~1 = r 2
SOL‘UTlUN
, Step 1. List restrictions «nth: variable.
1 __ S
‘+:‘E
This dmn'nur luld
qlllﬂiffO. The restrictinn is x ¢ 0. Step 2‘ Mdﬂpb' both sides by line LCD. The denominators are x and 2.111in the
LCD is 2x. We multiply hath sides by 21:. l 5
x ‘i‘ I = '2‘. x 235 D Thii is the: g‘wnéquaﬁzﬁ.
ﬂ‘u .5“
231:1 + T; = 232' Multiply hath QUE! by ti’ﬁ LCD.
1 ___ ' 5 Us: the diatrith From
2x»x+2px —2.xt2 ontmmﬂua
2x2 + 2 = 5x ‘ ﬁimpllﬁk Step 3. Solve the resulting equation. Can you see that we have a quadratic equation?
Write the mnation in standard form and salve far 1’. 2:2 m 5: + 2 = 0 sum: Exfrmn bath sum.
(21 — l)[x  Z) = 0 Factor.
21 "l = D at x * Z ”= U Eatnd‘iﬁutwcquaitoﬂ.
2.2 2 1 x = 2 50km tha mauln‘ngequarirans.
x z 1
2 Sup 4. Check limpused Ioluﬂnns in the original equation. The prnpcmd mluﬁansé
and 2, are not part of the restrictij that x .1 U. NeiLhar makes a denuminator
in the original amatiun equal to 22m. MatlZO Chapter 11 — Section 6 Page 25‘
Rational Equations EXAMPLES:
7.x:  4 n 9 _‘ i
6‘ 5x “ 5 x
STEP 1: List the restriction on the variable:
M0 mm WFS ¢ 0 W
0
S" K 3% 0 0 X :7” X 0
X¢0 \ xaa
STEP 2: Clear the equation by multiplying both sides by the LCD. Which is Using the distributive property. M33? J mi? r {was 7xaq ;r X(q)ra574)
'7X‘/: ?>< ’40 STEP 3: Solve the equation.
—;. X — 4/ ~ ' 9L 0
——— a X: —~ /Q
STEP 4: Exclude those value(s) for the variable that make the denominator equal to 0 x¢0 styﬂaj< MatlZO Chapter 11 — Section 6 Page 244' EXAMPLES:
3x 4
. + =
m .r 4— 1 x  2 3
STEP 1: List the restriction on the variable:
06w Wait/V5 *7”; 0 0
><+l ¢ o X ’9“ 7“
X354 X 75 L STEP 2: Clear the equation by multiplying both sides by the LCD. Which is (xiii Using the distributive property. WW1) 33/11 {— (XﬂWib/izl: 3 (Al‘lﬂxr‘eu) 3 (K—l—IHX‘Jvl STEP 3: Solve the equation. (2
STEP 4: Exclude those value(s) for the variable that make the denominator equal to O Mat120 Chapter 11 — Section 6 Page 9.3
Rational Equations
EXANIPLES:
32 4 2 .L ls'xz—25=x+5 ' .t——5 STEP 1: 3:. 5' o xts’%o xaraéa 5,,
(xﬂcr—fs’) :0 Kﬁf’id X 17" #«d K d
K 7’: 5’ ><+—s* wr 29h: STEP 2: Clear the equation by multiplying both sides by the LCD. Which is (K‘s—J Using the distributive property. .7 imﬂﬁgg) 39‘ :z: 4‘ (X—E‘.) 7L 20(25—7
409,10 + 509/0 f7’17L_:..— QM STEP 3: Solve the equation. STEP 4: Exclude those value(s) for the variable that make the denominator equal to 0 xaeS'Xgé—S ﬂak; / Mat120 Chapter 11 — Section 6 Page 2 3/ EXAMPLES:
4x 12 4x2 + 36 29' x+3~x3= ,tfz9 STEP 1: List the restriction on the variable:
mesﬁ 7a m2 5 »
2<+5 $0 X~3 #0 X “~77” ,
(X—b)bc+3 #0 3
x+ 4» X? 5 X46 3 X9613 STEP 2: Clear the equation by multiplying both sides by the LCD. Which is [(4 “i 2 g Using the distributive property. exam)” MOW»): STEP 3: Solve the equation. :1. ,_. 5
STEP 4: Exclude those value(s) for the variable that make the denominator equal to 0 W
#2 x¢ﬁ3 W X2v3 u ...
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This note was uploaded on 05/05/2008 for the course MAT 120/222/10 taught by Professor None during the Spring '08 term at ASU.
 Spring '08
 None

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