120_11.6_notes

120_11.6_notes - Mat120 Chapter 11 Section 6 Page 2‘...

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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‘UTl-UN , Step 1. List restrictions «nth: variable. 1 __ S ‘+:‘E This dmn'nur luld qlllfliff-O. 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‘ngequar-irans. x z 1 2 Sup 4. Check limp-used 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 (A-l‘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,, (x-flcr—fs’) :0 Kfif’id X 17" #«d K d K 7’: 5’ ><+—-s* wr 29-h: 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~x-3= ,tfz--9 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.

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120_11.6_notes - Mat120 Chapter 11 Section 6 Page 2‘...

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