Qhov sib npaug uas tsim nyog yog ib feem nrog ib lossis ntau qhov sib txawv hauv cov lej lossis cov lej. Ib qho kev sib npaug uas tsim nyog yog ib feem uas cuam tshuam nrog tsawg kawg ib qho kev ua zauv uas tsim nyog. Zoo li cov lej sib npaug algebraic zoo ib yam, qhov sib npaug uas muaj txiaj ntsig tau daws los ntawm kev ua haujlwm tib yam ntawm ob sab ntawm qhov sib npaug kom txog thaum qhov sib txawv tuaj yeem hloov pauv mus rau ob sab ntawm qhov sib npaug. Ob txoj hauv kev tshwj xeeb, hla kev sib npaug thiab nrhiav qhov tsawg tshaj plaws ntawm cov lej, yog txoj hauv kev muaj txiaj ntsig zoo rau txav cov kev hloov pauv thiab daws qhov sib npaug uas tsim nyog.
Kauj ruam
Txoj Kev 1 ntawm 2: Hla Kev Sib Cais
Kauj Ruam 1. Yog xav tau, rov kho koj qhov kev ua kom tau ib feem ntawm ib sab ntawm qhov kev ua zauv
Hla kev sib npaug yog txoj hauv kev nrawm thiab yooj yim los daws qhov sib npaug uas tsim nyog. Hmoov tsis zoo, txoj hauv kev no tsuas tuaj yeem siv rau qhov sib npaug uas muaj tsawg kawg ib qho kev sib npaug uas tsim nyog lossis feem ntawm txhua sab ntawm qhov kev ua zauv. Yog tias koj qhov kev ua zauv tsis tau raws li qhov xav tau ntawm cov khoom hla, koj yuav tsum tau siv algebraic ua haujlwm kom txav cov khoom mus rau qhov chaw raug.
-
Piv txwv, qhov sib npaug (x + 3)/4-x/(-2) = 0 tuaj yeem yooj yim muab tso rau hauv cov khoom hla los ntawm kev ntxiv x/(-2) rau ob sab ntawm qhov sib npaug, kom nws dhau los (x + 3)/4 = x/(-2).
Nco ntsoov tias cov zauv zauv thiab tus lej tuaj yeem hloov pauv mus ua ib feem los ntawm kev muab tus lej 1. (x + 3)/4 - 2, 5 = 5, piv txwv li, tuaj yeem rov sau dua li (x + 3)/4 = 7, 5/ 1, ua kom nws txaus siab hla kev sib npaug
- Qee qhov sib npaug uas tsim nyog tsis tuaj yeem raug txo kom yooj yim rau hauv daim ntawv uas muaj ib feem lossis qhov sib npaug uas tsim nyog ntawm txhua sab. Hauv cov xwm txheej zoo li no, siv tib txoj kev faib ua feem tsawg.
Kauj Ruam 2. Hla hla
Hla hla txhais tau tias ua kom sib npaug ntawm ib tus lej ntawm ib feem los ntawm tus lej ntawm lwm feem thiab rov ua dua. Muab tus zauv faib ua feem ntawm sab laug los ua tus faib ua feem ntawm sab xis. Rov ua dua nrog tus lej faib sab xis nrog tus lej faib sab laug.
Hla kev ua haujlwm sib npaug raws li cov hauv paus ntsiab lus algebraic. Rational equation thiab lwm yam zauv tuaj yeem ua rau tsis sib faib los ntawm kev muab lawv faib los ntawm cov lej. Cov khoom hla yog qhov yooj yim txoj hauv kev los sib npaug ob sab ntawm qhov sib npaug los ntawm ob qho lej. Tsis ntseeg? Sim nws - koj yuav tau txais qhov txiaj ntsig zoo ib yam tom qab ua kom yooj yim dua
Kauj Ruam 3. Ua kom ob yam khoom sib npaug sib npaug
Tom qab hla kev sib tw, koj yuav tau txais ob qhov txiaj ntsig sib npaug. Ua kom lawv sib npaug sib luag thiab ua kom yooj yim los ua qhov sib npaug yooj yim li sai tau.
Piv txwv li, yog tias koj thawj qhov kev sib npaug yog (x+3)/4 = x/(-2), tom qab hla kev sib npaug, koj qhov kev ua zauv tshiab dhau los -2 (x+3) = 4x. Yog tias koj xav tau, koj tseem tuaj yeem sau nws li -2x - 6 = 4x
Kauj Ruam 4. Nrhiav tus nqi ntawm koj qhov sib txawv
Siv algebraic ua haujlwm los nrhiav tus nqi ntawm koj qhov kev ua zauv sib txawv. Nco ntsoov tias, yog x tshwm ntawm ob sab ntawm kab zauv, koj yuav tsum ntxiv lossis rho x los ntawm ob sab ntawm qhov sib npaug kom x tawm ntawm ib sab ntawm qhov sib npaug.
Hauv peb qhov piv txwv, peb tuaj yeem faib ob sab ntawm qhov sib npaug ntawm -2, yog li x+3 = -2x. Rho tawm x los ntawm ob sab muab 3 = -3x. Thaum kawg, los ntawm kev faib ob sab los ntawm -3, qhov tshwm sim ua -1 = x, uas tuaj yeem sau ua x = -1. Peb tau pom tus nqi ntawm x, daws peb qhov kev sib npaug uas tsim nyog
Txoj Kev 2 ntawm 2: Nrhiav Qhov Tsawg Tshaj Lij Feem Ntau
Kauj Ruam 1. Paub lub sijhawm pes tsawg los siv tib tus lej me tshaj
Tib qho loj me me ntawm cov lej tuaj yeem siv los ua kom yooj yim sib npaug qhov muaj txiaj ntsig, ua rau lawv tshawb nrhiav qhov sib txawv qhov tseem ceeb. Nrhiav qhov tsawg tshaj plaws ntawm cov lej yog lub tswv yim zoo yog tias koj qhov sib npaug tsis tuaj yeem sau tau yooj yim raws li ib feem (thiab tsuas yog ib feem) ntawm txhua sab ntawm qhov sib npaug. Rau kev daws qhov sib npaug uas tsim nyog nrog peb lossis ntau qhov, qhov tsawg tshaj plaws sib faib yog qhov muaj txiaj ntsig. Txawm li cas los xij, txhawm rau daws qhov sib npaug uas muaj txiaj ntsig nrog tsuas yog ob ntu, nws nrawm dua los siv cov khoom hla.
Kauj Ruam 2. Txheeb tus lej ntawm txhua feem
Txheeb xyuas tus lej tsawg tshaj plaws uas txhua tus lej tuaj yeem faib thiab ua tus lej tag nrho. Tus lej no yog tus lej tsawg tshaj plaws rau koj qhov kev ua zauv.
- Qee zaum qhov tsawg tshaj plaws sib faib - uas yog, tus lej tsawg tshaj plaws uas muaj txhua yam hauv tus lej - yog pom meej. Piv txwv, yog tias koj qhov kev ua zauv yog x/3 + 1/2 = (3x + 1)/6, nws tsis nyuaj pom tus lej me tshaj plaws uas muaj tus lej 3, 2, thiab 6, uas yog tus lej 6.
- Txawm li cas los xij, feem ntau, qhov tsawg tshaj plaws ntawm qhov sib npaug ntawm qhov sib npaug tsis pom tseeb. Hauv qhov xwm txheej zoo li no, sim txheeb xyuas ntau ntxiv ntawm cov lej sib faib kom txog thaum koj pom tus lej uas muaj qhov tseem ceeb ntawm txhua lwm cov lej me me. Feem ntau, qhov sib faib tsawg tshaj plaws yog cov khoom lag luam ntawm ob tus lej. Piv txwv li, hauv kab zauv x/8 + 2/6 = (x-3)/9, qhov tsawg tshaj plaws sib faib yog 8*9 = 72.
- Yog tias ib lossis ntau ntawm koj qhov feem faib muaj qhov sib txawv, cov txheej txheem no nyuaj dua, tab sis ua tau. Hauv qhov xwm txheej zoo li no, qhov tsawg tshaj plaws ntawm cov lej yog qhov sib npaug (nrog qhov sib txawv) uas tau faib los ntawm tag nrho lwm cov lej. Piv txwv li hauv kab zauv 5/(x-1) = 1/x + 2/(3x), qhov sib faib tsawg tshaj plaws yog 3x (x-1) vim tias txhua tus lej tuaj yeem faib nws-faib los ntawm (x-1) muab 3x, faib los ntawm 3x muab (x-1), thiab faib los ntawm x muab 3 (x-1).
Kauj Ruam 3. Sib npaug txhua feem hauv qhov sib npaug uas tsim nyog los ntawm 1
Sib npaug txhua feem ntawm 1 zoo li tsis muaj txiaj ntsig. Tab sis ntawm no yog qhov dag. 1 tuaj yeem txhais tau tias yog tus lej uas zoo ib yam hauv tus lej thiab cov lej, xws li -2/2 thiab 3/3, uas yog txoj hauv kev raug sau 1. Txoj kev no siv qhov zoo ntawm lwm txoj kev txhais. Sib npaug txhua feem hauv koj qhov kev ua lej sib npaug los ntawm 1, sau tus lej 1 uas thaum sib tw los ntawm tus lej faib ua qhov tsawg tshaj plaws sib faib.
- Hauv peb qhov piv txwv yooj yim, peb yuav sib npaug x/3 los ntawm 2/2 kom tau 2x/6 thiab sib npaug 1/2 los ntawm 3/3 kom tau 3/6. 2x + 1/6 twb muaj qhov sib npaug me me tshaj plaws, uas yog 6, yog li peb tuaj yeem sib npaug nws li 1/1 lossis tso nws ib leeg.
- Hauv peb qhov piv txwv nrog qhov sib txawv hauv cov lej ntawm cov feem, cov txheej txheem yog nyuab dua. Txij li thaum peb tus lej me tshaj yog 3x (x-1), peb sib npaug txhua qhov sib npaug uas muaj txiaj ntsig los ntawm qee yam uas rov qab 3x (x-1). Peb yuav muab 5/(x-1) los ntawm (3x)/(3x) uas muab 5 (3x)/(3x) (x-1), sib npaug 1/x los ntawm 3 (x-1)/3 (x- 1) uas muab 3 (x-1)/3x (x-1), thiab sib npaug 2/(3x) los ntawm (x-1)/(x-1) muab 2 (x-1)/3x (x-1)).
Kauj Ruam 4. Yooj yim thiab nrhiav tus nqi x
Tam sim no, txij li txhua feem ntawm koj qhov kev ua zauv muaj qhov sib npaug sib npaug, koj tuaj yeem tshem tus lej ntawm koj qhov kev ua zauv thiab daws rau tus lej. Muab ob sab ntawm qhov sib npaug kom tau tus lej lej. Tom qab ntawd, siv algebraic ua haujlwm txhawm rau nrhiav tus nqi x (lossis yam sib txawv uas koj xav daws) ntawm ib sab ntawm qhov sib npaug.
- Hauv peb qhov piv txwv yooj yim, tom qab muab tag nrho txhua ntu los ntawm daim ntawv xaiv 1, peb tau txais 2x/6 + 3/6 = (3x + 1)/6. Ob feem ntxiv tau yog tias lawv muaj cov lej sib npaug, yog li peb tuaj yeem yooj yim ua qhov sib npaug rau (2x+3)/6 = (3x+1)/6 yam tsis hloov tus nqi. Muab ob tog sib npaug los ntawm 6 kom tshem tus lej, yog li qhov tshwm sim yog 2x+3 = 3x+1. Rho tawm 1 los ntawm ob sab kom tau 2x+2 = 3x, thiab rho 2x los ntawm ob sab kom tau 2 = x, uas tuaj yeem sau ua x = 2.
- Hauv peb qhov piv txwv nrog qhov sib txawv hauv cov lej, peb qhov kev ua zauv tom qab sib npaug 1 ua 5 (3x)/(3x) (x-1) = 3 (x-1)/3x (x-1) + 2 (x-1)) /3x (x-1). Muab tag nrho txhua qhov los ntawm qhov sib piv me me tshaj plaws, tso cai rau peb tshem tawm tus lej, ua 5 (3x) = 3 (x-1) + 2 (x-1). Qhov no kuj siv rau 5x = 3x -3 + 2x -2, uas yooj yim rau 15x = x -5. Kev rho tawm x los ntawm ob sab muab 14x = -5, uas, thaum kawg, yooj yim rau x = -5/14.
Lub tswv yim
- Thaum koj tau daws qhov sib txawv, txheeb xyuas koj cov lus teb los ntawm ntsaws qhov sib txawv tus nqi rau hauv qhov qub zauv. Yog tias koj qhov txiaj ntsig sib txawv raug, koj tuaj yeem ua kom yooj yim rau koj qhov kev ua zauv yooj yim rau hauv nqe lus yooj yim uas ib txwm sib npaug 1 = 1.
- Nco ntsoov tias koj tuaj yeem sau ib qho ntau tus lej raws li qhov muaj feem sib npaug; muab nws tso rau saum cov denominator 1. Yog li x+3 thiab (x+3)/1 muaj tus nqi zoo ib yam, tab sis qhov sib npaug thib ob tuaj yeem raug cais ua qhov sib npaug uas tsim nyog vim tias nws tau sau ua ib feem.
