Algebraic feem feem yuav zoo li nyuaj thiab hem rau cov tub ntxhais kawm uas tsis tau npaj tseg. Algebraic fractions tau ua los ntawm kev sib xyaw ntawm cov lej, tus lej, thiab txawm tias tus lej nthuav tawm yog li lawv tuaj yeem nkag siab yuam kev. Hmoov zoo, txawm li cas los xij, cov cai rau kev yooj yim rau feem feem ntau, xws li 15/25, kuj tseem siv rau cov lej algebraic.
Kauj ruam
Txoj Kev 1 ntawm 3: Yooj Yim Yooj Yim
Kauj Ruam 1. Paub ntau yam ntsiab lus hauv cov lej zauv lej
Cov nqe lus hauv qab no feem ntau siv hauv teeb meem cov lej algebraic:
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Tus lej:
sab saum toj ntawm feem (piv txwv: '' '(x+5)' ''/(2x+3)).
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Kev faib ua feem:
hauv qab ntawm feem (piv txwv: (x+5)/`` (2x+3) '' '').
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Cov feem sib faib:
tus lej uas tuaj yeem faib rau saum thiab hauv qab ntawm ib feem. Piv txwv: qhov feem sib faib ntawm feem 3/9 yog 3 vim tias 3 thiab 9 tau faib ua 3.
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Qhov tseeb:
cov lej uas tuaj yeem faib tus lej kom txog thaum nws tas. Piv txwv: yam 15 yog 1, 3, 5, thiab 15. Qhov 4 yog 1, 2, thiab 4.
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Qhov yooj yim feem:
coj txhua yam xwm txheej ib txwm thiab muab tib qhov sib txawv ua ke (5x + x = 6x) kom txog thaum koj tau txais cov teeb meem yooj yim tshaj plaws, sib npaug, lossis feem. Yog tias tsis muaj kev suav ntau dua uas tuaj yeem ua tiav, qhov feem ntawm nws qhov yooj yim tshaj plaws.
Kauj Ruam 2. Rov kawm paub yuav ua li cas yooj yim rau feem feem ntau
Algebraic fractions tau yooj yim hauv tib txoj kev uas lawv ua kom yooj yim sib npaug. Piv txwv li, kom yooj yim 15/35, nrhiav cov feem sib faib cov feem. Qhov feem sib faib ntawm feem 15/35 yog 5. Yog li, faib tawm 5 los ntawm cov feem
15 → 5 * 3
35 → 5 * 7
Tam sim no, tshem tawm cov feem sib faib. Hauv qhov piv txwv saum toj no, tshem ob qho 5s. Yog li, daim ntawv yooj yim 15/35 yog 3/7.
Kauj Ruam 3. Siv qhov feem ntau tawm ntawm cov zauv zauv lej hauv tib txoj kev ib yam li cov lej ib txwm
Hauv qhov piv txwv dhau los, 5 tuaj yeem txiav tawm tau yooj yim ntawm 15. Tib txoj hauv kev siv rau cov kab lus nyuab dua, xws li 15x - 5. Nrhiav qhov sib txuam ntawm ob tus lej hauv qhov teeb meem. 5 yog ib qho xwm txheej uas tuaj yeem faib ob qho 15x thiab -5. Ib yam li ua ntej, tshem tawm cov xwm txheej ib txwm thiab sib npaug los ntawm "qhov seem".
15x - 5 = 5 * (3x - 1) Txheeb los ntawm kev sib npaug 5 los ntawm cov lus qhia tshiab. Yog tias nws raug, qhov tshwm sim zoo ib yam li thawj qhov kev qhia (ua ntej qhov sib xws, uas yog 5, tsis suav nrog).
Kauj Ruam 4. Ntxiv rau qhov tseem ceeb hauv daim ntawv ntawm cov lej zoo tib yam, cov lej tsis yooj yim kuj tseem tuaj yeem tso tseg
Algebraic fraction simplification siv tib lub hauv paus ntsiab lus zoo ib yam li ib feem me me. Lub hauv paus ntsiab lus no yog txoj hauv kev yooj yim tshaj plaws los ua piv txwv yooj yim. Piv txwv li:
(x+2) (x-3)
(x+2) (x+10)
muaj nyob hauv tus lej (sab saum toj ntawm cov feem) thiab cov lej (hauv qab ntawm cov feem). Yog li, (x+2) tuaj yeem raug rho tawm kom yooj yim rau cov lej algebraic, ib yam li tshem tawm thiab tshem tawm 5 los ntawm 15/35:
(x+2) (x-3) → (x-3)
(x+2) (x+10) → (x+10) Yog li, cov lus teb kawg yog: (x-3)/(x+10)
Txoj Kev 2 ntawm 3: Simplifying Algebraic Fractions
Kauj Ruam 1. Nrhiav qhov feem ntau ntawm tus zauv (sab saum toj ntawm cov feem)
Thawj kauj ruam hauv kev yooj yim ib feem algebraic yog ua kom yooj yim rau txhua feem ntawm cov feem. Ua tus lej lej ua ntej. Tshem tawm cov xwm txheej ib txwm kom txog thaum koj tau txais cov lus yooj yim tshaj plaws. Piv txwv:
9 x3; ua
15 x+6 po
Ua tus lej tus lej: 9x -3. Qhov sib npaug ntawm 9x thiab -3 yog 3. Qhov zauv tawm tus lej 3 los ntawm 9x -3 ua 3*(3x -1). Sau tus lej zauv tshiab qhia rau qhov feem:
3 (3x-1)
15 x+6 po
Kauj Ruam 2. Nrhiav qhov sib koom ua ke hauv cov lej (hauv qab ntawm cov feem)
Txuas ntxiv mus ua haujlwm ntawm qhov piv txwv teeb meem saum toj no, xyuam xim rau tus lej, 15x+6. Ib zaug ntxiv, nrhiav tus lej uas faib ob ntu ntawm qhov kev nthuav qhia. Qhov feem ntau ntawm 15x thiab 6 yog 3. Factor 3 tawm ntawm 15x+6 ua 3*(5x+2). Sau cov lus sib cais tshiab ntawm qhov feem:
3 (3x-1)
3 (5x+2) (4x+5)
Kauj Ruam 3. Tshem tawm cov lej qub
Cov kauj ruam no ua kom yooj yim dua. Yog tias tus lej thiab cov lej muaj tib tus lej, tshem tus lej. Hauv qhov piv txwv, tus lej 3 hauv tus lej thiab cov lej tuaj yeem tso tseg tau.
3 (3x-1) → (3x-1)
3 (5x+2) → (4x+5)
Kauj Ruam 4. Txheeb xyuas tias cov lej lej sib npaug yog qhov yooj yim tshaj plaws
Qhov yooj yim algebraic feem feem tsis muaj qhov cuam tshuam ntau hauv cov lej lossis cov lej. Nco ntsoov, yam tsis tuaj yeem raug rho tawm. Hauv qhov teeb meem piv txwv, x tsis tuaj yeem txiav tawm ntawm 3x thiab 5x vim tias cov kab lus ua tiav yog (3x-1) thiab (5x+2). Yog li, ob kab lus twb yog qhov yooj yim tshaj plaws thiab tau txais lus teb kawg:
(3 x 1)
(4x+5)
Kauj Ruam 5. Ua cov lus nug xyaum
Txoj hauv kev zoo tshaj los tswj lub ntsiab lus no yog ua kom xyaum ua haujlwm ntawm cov lej yooj yooj yim ib feem. Ua ob lo lus nug hauv qab no; Cov lus teb tseem ceeb yog hauv qab cov lus nug.
4x (x+2) (x-13)
(4x+8) Teb:
(x = 13) - np.
2x ua2-x ib
5 x ygo Teb:
(2x-1)/5
Txoj Kev 3 ntawm 3: Ua Teeb Meem Ntau Dhau
Kauj Ruam 1. “Hloov” qhov feem ntawm qhov faib tawm los ntawm tus lej tsis zoo
Teeb meem piv txwv:
3 (x -4)
5 (4x-x)
(x-4) thiab (4-x) '' yuav luag '' yog tib yam. (x-4) thiab (4-x) tsis tuaj yeem raug tshem tawm vim tias lawv tau thim rov qab. Txawm li cas los xij (x-4) tuaj yeem hloov pauv mus rau -1 * (4-x), ib yam li hloov pauv (4 + 2x) mus rau 2 * (2 + x). Txoj hauv kev no hu ua "cais tawm tus lej tsis zoo".
-1*3 (4x-x)
5 (4x-x)
Tam sim no ob qho (4-x) tuaj yeem raug rho tawm:
-1*3 (4x-x)
5 (4x-x)
Yog li, qhov lus teb kawg yog - 3/5
Kauj Ruam 2. Txheeb xyuas daim ntawv ntawm qhov sib txawv ntawm ob lub xwmfab thaum ua haujlwm ntawm qhov teeb meem
Daim ntawv ntawm qhov sib txawv ntawm ob lub xwmfab yog ib feem plaub rho tawm lwm (a.)2 -b2). Daim ntawv ntawm qhov sib txawv ntawm ob lub yeej ib txwm yooj yim ua ob ntu, ntxiv thiab rho tawm cov hauv paus cag:
a2 -b2 = (a+b) (a-b) Cov mis no tseem ceeb heev rau kev nrhiav cov hauv paus hauv algebraic fractions.
Piv txwv: x2 -25 = (x+5) (x-5)
Kauj Ruam 3. Ua kom yooj yim rau cov lus piav qhia polynomial
Polynomial yog ib qho nyuaj piav qhia algebraic uas muaj ntau dua ob nqe lus, piv txwv li x2 + 4x + 3. Hmoov zoo, feem ntau cov npe ntawm polynomials tuaj yeem ua kom yooj yim los ntawm kev txheeb xyuas cov lej. Piv txwv: x2 + 4x+ 3 tuaj yeem ua kom yooj yim rau (x+ 3) (x+ 1).
Kauj Ruam 4. Nco ntsoov, qhov sib txawv kuj tseem tuaj yeem muab cais tawm
Qhov no yog qhov tseem ceeb heev, tshwj xeeb tshaj yog hauv kab lus uas muaj cov lus nthuav tawm. Piv txwv: x4 +xwm2. Txheeb cais tawm qhov nthuav dav tshaj plaws. Yog li, x4 +xwm2 = xwm2(xwm2 + 1).
Lub tswv yim
- Ib txwm siv qhov tseem ceeb tshaj plaws thaum ua kom yooj yim kom ntseeg tau tias cov lus teb kawg yog hauv daim ntawv yooj yim tshaj plaws.
- Txheeb xyuas cov lus teb los ntawm kev sib koom nrog lwm yam ntxiv. Yog tias koj cov lus teb raug lawm, qhov sib npaug rov qab los qhia tawm yav dhau los.
