Cov lus piav qhia yuav tsum tau ua kom yooj yim rau tib yam yooj yim. Qhov no yog txheej txheem yooj yim yooj yim yog tias tib yam tseem ceeb yog ib qho xwm txheej ib zaug, tab sis cov txheej txheem tau txais me ntsis ntxiv yog tias qhov xwm txheej suav nrog ntau nqe lus. Nov yog yam koj yuav tsum tau ua, nyob ntawm seb hom kev xav uas koj tab tom cuam tshuam nrog.
Kauj ruam
Txoj Kev 1 ntawm 3: Mononomial Rational Expressions (Single Term)
Kauj Ruam 1. Txheeb xyuas qhov teeb meem
Cov lus piav qhia uas tsuas yog suav nrog monomials (ib nqe lus) yog cov kab lus yooj yim tshaj plaws kom yooj yim. Yog tias ob nqe lus hauv kab lus tsuas muaj ib nqe lus xwb, txhua yam koj yuav tsum ua yog yooj yim piv cov lej thiab cov lej rau tib nqe qis tshaj.
- Nco ntsoov tias mono txhais tau tias "ib qho" lossis "ib leeg" hauv cov ntsiab lus no.
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Piv txwv:
4x/8 x 2
Kauj Ruam 2. Tshem tawm txhua qhov kev hloov pauv uas zoo ib yam
Saib cov ntawv hloov pauv hauv qhov kev qhia. Yog tias qhov sib txawv sib xws tshwm nyob rau hauv ob tus lej thiab cov lej, koj tuaj yeem tso tseg qhov sib txawv no ntau zaus raws li nws tshwm sim hauv ob qho ntawm qhov kev qhia.
- Hauv lwm lo lus, yog qhov sib txawv tshwm sim ib zaug hauv qhov qhia hauv tus lej thiab ib zaug hauv cov lej, qhov sib txawv tuaj yeem raug tshem tawm tag nrho: x/x = 1/1 = 1
- Txawm li cas los xij, yog tias muaj qhov sib txawv tshwm sim ntau zaus nyob rau hauv ob tus lej thiab cov lej, tab sis tsuas yog tshwm sim tsawg kawg ib zaug hauv lwm qhov ntawm qhov kev hais tawm, rho tawm cov lus piav qhia uas qhov sib txawv muaj nyob hauv ntu me ntawm kev nthuav qhia los ntawm cov lus piav qhia uas qhov sib txawv muaj nyob hauv qhov loj dua: x^4/ x^2 = x^2/1
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Piv txwv:
x/x^2 = 1/x
Kauj Ruam 3. Ua kom yooj yim rau cov lus yooj yim
Yog tias tus lej ntawm tus lej muaj qhov zoo ib yam, faib qhov tsis tu ncua hauv tus lej thiab qhov tsis tu ncua hauv cov lej los ntawm tib yam, txhawm rau ua kom yooj yim feem rau nws daim ntawv yooj yim tshaj plaws: 8/12 = 2/3
- Yog tias qhov nyob hauv qhov kev xav tsis muaj qhov zoo ib yam, tom qab ntawd lawv tsis tuaj yeem yooj yim: 7/5
- Yog tias ib qho tas mus li faib los ntawm lwm qhov tsis tu ncua, nws suav tias yog qhov sib npaug: 3/6 = 1/2
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Piv txwv:
4/8 = 1/2
Kauj Ruam 4. Sau koj cov lus teb zaum kawg
Txhawm rau txiav txim siab koj cov lus teb kawg, koj yuav tsum rov ua ke cov kev hloov pauv yooj yim thiab qhov yooj yim tsis tu ncua.
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Piv txwv:
4x/8^2 = 1/2 x
Txoj Kev 2 ntawm 3: Cov zauv zauv thiab Polynomial Rational Expressions nrog Mononomial Factors (Ib Zaug)
Kauj Ruam 1. Txheeb xyuas qhov teeb meem
Yog tias ib feem ntawm qhov kev xav tau yog monomial (ib lo lus), tab sis lwm qhov yog ob tus lej lossis ntau tus lej, koj yuav xav tau ua kom yooj yim cov lus los ntawm kev hais qhia monomial (ib lub sij hawm) qhov uas tuaj yeem siv rau ob tus lej thiab tus lej
- Hauv cov ntsiab lus no, mono txhais tau tias "ib qho" lossis "ib leeg", bi txhais tau tias "ob", thiab poly txhais tau tias "ntau".
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Piv txwv:
(4x)/(3x + 6x^2)
Kauj Ruam 2. Tshaj tawm ib qho kev hloov pauv uas zoo ib yam
Yog tias muaj ib tsab ntawv sib txawv tshwm nyob rau txhua nqe lus ntawm qhov sib npaug, koj tuaj yeem suav qhov sib txawv ntawd raws li ib feem ntawm cov ntsiab lus tawm.
- Qhov no tsuas yog siv yog tias qhov sib txawv tshwm sim hauv txhua nqe lus ntawm qhov kev ua zauv: x/x^3 - x^2 + x = (x) (x^2 - x + 1)
- Yog tias ib qho ntawm cov ntsiab lus ntawm qhov sib npaug tsis muaj qhov sib txawv no, koj tsis tuaj yeem faib nws tawm: x/x^2 + 1
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Piv txwv:
x / (x + x^2) = [(x) (1)] / [(x) (1 + x)]
Kauj Ruam 3. Tshaj tawm txhua yam uas zoo ib yam
Yog hais tias tus lej zauv nyob hauv txhua nqe lus muaj tib yam, faib txhua qhov nyob hauv cov ntsiab lus los ntawm tib yam, txhawm rau ua kom yooj yim tus lej thiab cov lej.
- Yog tias ib qho tas li faib los ntawm lwm qhov tsis tu ncua, nws suav tias yog qhov sib npaug: 2 / (2 + 4) = 2 * [1 / (1 + 2)]
- Nco ntsoov tias qhov no tsuas siv tau yog tias txhua nqe lus hauv qhov kev hais tawm muaj tsawg kawg ib yam hauv ib qho: 9 / (6 - 12) = 3 * [3 / (2 - 4)]
- Qhov no tsis siv yog tias ib qho ntawm cov ntsiab lus hauv kev qhia tsis muaj qhov zoo ib yam: 5 / (7 + 3)
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Piv txwv:
3/(3 + 6) = [(3)(1)] / [(3)(1 + 2)]
Kauj Ruam 4. Txheeb tawm cov ntsiab lus sib npaug
Recombine cov kev hloov pauv yooj yim thiab cov qauv yooj yim los txiav txim siab tib yam. Tshem tawm qhov tseem ceeb no los ntawm kev qhia, tawm ntawm qhov sib txawv thiab qhov tsis sib xws uas tsis zoo ib yam hauv txhua nqe lus.
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Piv txwv:
(3x) / (3x + 6x^2) = [(3x) (1)] / [(3x) (1 + 2x)]
Kauj Ruam 5. Sau koj cov lus teb zaum kawg
Txhawm rau txiav txim siab qhov lus teb kawg, tshem tawm cov xwm txheej ib txwm los ntawm kev qhia.
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Piv txwv:
[(3x) (1)] / [(3x) (1 + 2x)] = 1 / (1 + 2x)
Txoj Kev 3 ntawm 3: Cov zauv zauv lossis ntau lub ntsiab lus hais txog zauv nrog zauv zauv
Kauj Ruam 1. Txheeb xyuas qhov teeb meem
Yog tias tsis muaj ib lo lus monomial (ib lo lus) hauv qhov kev xav uas muaj txiaj ntsig, koj yuav tsum ua txhaum tus lej thiab feem rau hauv cov lej zauv.
- Hauv cov ntsiab lus no, mono txhais tau tias "ib qho" lossis "ib leeg", bi txhais tau tias "ob", thiab poly txhais tau tias "ntau".
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Piv txwv:
(x^2 - 4) / (x^2 - 2x - 8)
Kauj Ruam 2. Txheeb tus lej mus rau hauv nws cov lej zauv
Txhawm rau txhawm rau tus lej mus rau nws cov yam, koj yuav tsum txiav txim siab qhov ua tau rau koj qhov sib txawv, x.
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Piv txwv:
(x^2 - 4) = (x - 2) * (x + 2)
- Txhawm rau nrhiav tus nqi ntawm x, koj yuav tsum txav qhov tas mus li rau ib sab thiab qhov sib txawv mus rau lwm qhov: x^2 = 4x
- Yooj yim x rau lub zog ntawm ib qho los ntawm kev nrhiav lub hauv paus cuav ntawm ob sab: x^2 = 4x
- Nco ntsoov tias lub hauv paus cag ntawm txhua tus lej tuaj yeem ua qhov zoo lossis tsis zoo. Yog li, cov lus teb tau rau x yog: - 2, +2
- Yog li, thaum piav qhia (x^2 - 4) yog yam, yam yog: (x - 2) * (x + 2)
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Txheeb xyuas koj ob qho tib si los ntawm kev muab lawv ntau ntxiv. Yog tias koj tsis paub tseeb tias koj tau muab ib feem ntawm qhov kev hais qhia qhov tseeb los raug lossis tsis yog, koj tuaj yeem muab cov xwm txheej no kom ntseeg tau tias qhov txiaj ntsig zoo ib yam li thawj qhov kev hais tawm. Nco ntsoov siv PLDT yog tsim nyog siv: pthawj, lsab nraum, dntuj, tkawg.
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Piv txwv:
(x - 2) * (x + 2) = x^2 + 2x - 2x - 4 = x^2 - 4
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Kauj Ruam 3. Txheeb cais tus lej rau hauv nws cov lej zauv
Txhawm rau txhawm rau faib cov lej rau hauv nws cov xwm txheej, koj yuav tsum txiav txim siab qhov ua tau rau koj qhov sib txawv, x.
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Piv txwv:
(x^2 - 2x - 8) = (x + 2) * (x - 4x)
- Txhawm rau nrhiav tus nqi ntawm x, koj yuav tsum txav qhov tas mus li mus rau ib sab thiab tshem tag nrho cov ntsiab lus, suav nrog qhov sib txawv, mus rau lwm sab: x^2 2x = 8
- Ua kom tiav cov xwm txheej ntawm cov coefficients ntawm x lub sij hawm thiab ntxiv qhov tseem ceeb rau ob sab: x^2 2 4x + 1 = 8 + 1
- Yooj yim rau sab xis thiab sau lub xwmfab zoo tshaj plaws ntawm sab xis: (x 1)^2 = 9
- Nrhiav cov hauv paus plaub fab ntawm ob sab: x 1 = √ √9
- Nrhiav tus nqi x: x = 1 ± √9
- Zoo li ib qho kev ua lej sib npaug, x muaj ob txoj hauv kev daws tau.
- x = 1 - 3 = -2
- x = 1 + 3 = 4
- Yog li ntawd, (x^2 - 4x - 8) tau muab tso rau hauv (x + 2) * (x - 4)
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Txheeb xyuas koj ob qho tib si los ntawm kev muab lawv ntau ntxiv. Yog tias koj tsis paub tseeb tias koj tau muab ib feem ntawm qhov kev hais qhia qhov tseeb los raug lossis tsis yog, koj tuaj yeem muab cov xwm txheej no kom ntseeg tau tias qhov txiaj ntsig zoo ib yam li thawj qhov kev hais tawm. Nco ntsoov siv PLDT yog tsim nyog siv: pthawj, lsab nraum, dntuj, tkawg.
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Piv txwv:
(x + 2) * (x - 4) = x^2 - 4x + 2x - 8 = x^2 - 2x - 8
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Kauj Ruam 4. Tshem tawm tib yam
Nrhiav tus lej zauv, yog tias muaj, uas zoo ib yam hauv ob tus lej thiab cov lej. Tshem tawm qhov xwm txheej no los ntawm kev qhia tawm, ua rau cov lej binomial tsis sib xws.
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Piv txwv:
[(x - 2) (x + 2)] / [(x + 2) (x - 4)] = (x + 2) * [(x - 2) / (x - 4)]
Kauj Ruam 5. Sau koj cov lus teb zaum kawg
Txhawm rau txiav txim siab qhov lus teb kawg, tshem tawm cov xwm txheej ib txwm los ntawm kev qhia.
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Piv txwv:
(x + 2) * [(x - 2) / (x - 4)] = (x - 2) / (x - 4)
