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IvidAwrQIAW dy nW hrpRIq isMG, sqnwm isMG, swihl kumwr, gursyvk isMG hrpRIq isMG, sqnwm isMG, swihl kumwr, gursyvk isMG,byAMq isMG, gurdIp kOr, nvjoq kOr,

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Presentation on theme: "IvidAwrQIAW dy nW hrpRIq isMG, sqnwm isMG, swihl kumwr, gursyvk isMG hrpRIq isMG, sqnwm isMG, swihl kumwr, gursyvk isMG,byAMq isMG, gurdIp kOr, nvjoq kOr,"— Presentation transcript:

1 ividAwrQIAW dy nW hrpRIq isMG, sqnwm isMG, swihl kumwr, gursyvk isMG hrpRIq isMG, sqnwm isMG, swihl kumwr, gursyvk isMG,byAMq isMG, gurdIp kOr, nvjoq kOr, nvpRIq kOr, mnpRIq kOr,,byAMq isMG, gurdIp kOr, nvjoq kOr, nvpRIq kOr, mnpRIq kOr, pRBjoq kOr pirmyX ivAMjk jmwq 10vIN ivSw - gixq srkwrI hweI skUl lOt, pitAwlw

2 ivSw sUcI pirmyX ivAMjkW dw joVPl pirmyX ivAMjkW dw joVPl pirmyX ivAMjkW dw Gtwau pirmyX ivAMjkW dw Gtwau pirmyX ivAMjkW dw juVn Xog aou~lt pirmyX ivAMjkW dw juVn Xog aou~lt pirmyX ivAMjk joiVAW dw guxnPl pirmyX ivAMjk joiVAW dw guxnPl guxwqmk au~lt guxwqmk au~lt

3 (pirmyX ivAMjk) (pirmyX ivAMjk) ijs qrHW sMpUrn sMiKAwvW qo pirmyX sMiKAwvW bxdIAW hn[ ausy qrHW hI jykr p(x) Aqy q(x) doo bhupdW hox qW p(x)/q(x) nUM AsIN pirmyX ivAMjk khWgy[ieQy q(x) dw ZYr is&r bhupd hoxw zrUrI hY[pirmyX ivAMjk p(x)/q(x) iv`c p(x) nUuM AMS Aqy q(x) nUM hr ikhw jWdw hY[ ijs qrHW sMpUrn sMiKAwvW qo pirmyX sMiKAwvW bxdIAW hn[ ausy qrHW hI jykr p(x) Aqy q(x) doo bhupdW hox qW p(x)/q(x) nUM AsIN pirmyX ivAMjk khWgy[ieQy q(x) dw ZYr is&r bhupd hoxw zrUrI hY[pirmyX ivAMjk p(x)/q(x) iv`c p(x) nUuM AMS Aqy q(x) nUM hr ikhw jWdw hY[

4 audwhrx 3x+7/ x 2_ 5x+6 ie`k pirmyX ivAMjk hY[iesdw AMS iek do GwqI bhupd Aqy hr cwr GwqI bhupd hY[

5 pirmyX ivAMjk d~so? hyTW iliKAW iv~coN ikhVy pirmyX ivAMjk hn? hyTW iliKAW iv~coN ikhVy pirmyX ivAMjk hn? 5 x 2 +3x-4/x x 2 +3x-4/x 2 +2 au~qr: pirmyX ivAMjk hY[ au~qr: pirmyX ivAMjk hY[ x 3/2 +4x-7 x 3/2 +4x-7 au~qr: pirmyX ivAMjk hY[ au~qr: pirmyX ivAMjk hY[

6 bhupd hr ie~k GwqI Aqy do GwqI d~so? ie~k ivAwpk pirmyX ivAMjk ilKo ijs dw AMS do GwqI bhupd Aqy hr ie~k GwqI bhupd hovy[ ie~k ivAwpk pirmyX ivAMjk ilKo ijs dw AMS do GwqI bhupd Aqy hr ie~k GwqI bhupd hovy[ au~qr: ax 2 +bx+c/ax+b au~qr: ax 2 +bx+c/ax+b

7 inaUnqm pdW iv~c d~so? hyTW ilKy pirmyX ivAMjkW iv~coN d~so ik ikhVI Awpxy inaUnqm pdW iv~c hY[jo pirmyX ivAMjk Awpxy inaUnqm pdW iv`c nhIN hY aus nMU inaUnqm pdW iv~c drswau[ hyTW ilKy pirmyX ivAMjkW iv~coN d~so ik ikhVI Awpxy inaUnqm pdW iv~c hY[jo pirmyX ivAMjk Awpxy inaUnqm pdW iv`c nhIN hY aus nMU inaUnqm pdW iv~c drswau[ x 2 +1/x 2 -1=x 2 +1/x =(x 2 +1)/(x+1)(x-1) inaUnqm pdW iv`c hY[ x 2 +1/x 2 -1=x 2 +1/x =(x 2 +1)/(x+1)(x-1) inaUnqm pdW iv`c hY[

8 juVn Xog au`lt hyT iliKAW dy juVn Xog au`lt ilKo[ 1. X-2/X+4 =-(x-2)/x+4 au~qr =-x-2/x (7-3)/x+2 au~qr =7+3/x+2

9 pirmyX ivAMjkW dw joVPl pqw kro hyT ilKy pirmyX ivAMjk dw joVPl pqw kro? hyT ilKy pirmyX ivAMjk dw joVPl pqw kro? X-2/x+4,x+2/x+4 X-2/x+4,x+2/x+4 = x-2+x+2/x+4 = x-2+x+2/x+4 au~qr = 2x/x+4 au~qr = 2x/x+4

10 pirmyX ivAMjkW dw joVPl pqw kro hyT ilKy pirmyX ivAMjkW dw joVPl pqw kro[ hyT ilKy pirmyX ivAMjkW dw joVPl pqw kro[ 1. x-2/x+4,x+2x+4=x-2+x+2 /(x+4) 1. x-2/x+4,x+2x+4=x-2+x+2 /(x+4) au~qr :- 2x/x+4 au~qr :- 2x/x+4 2. x+7/x-2,x-9/x-2=x+7+x-9/x-2 au~qr: 2(x-1)/x-2 2. x+7/x-2,x-9/x-2=x+7+x-9/x-2 au~qr: 2(x-1)/x-2

11 pirmyX ivAMjkW dw Gtwau? hyT ilKy pirmyX ivAMjkW dw Gtwau kro: hyT ilKy pirmyX ivAMjkW dw Gtwau kro: 4x+5/x+2, 3x-1/x+2 4x+5/x+2, 3x-1/x+2 4x+5-3x+1/x+2 4x+5-3x+1/x+2 au~qr= x+6/x+2 au~qr= x+6/x+2

12 pirmyX ivAMjk joiVAW dw guxnPl hyT ilKy pirmyX ivAMjk joiVAW dw guxnPl pqw kro hyT ilKy pirmyX ivAMjk joiVAW dw guxnPl pqw kro x-3 / x+4, x+3 / x+2 x-3 / x+4, x+3 / x+2 (x) 2 -(3) 2 /x 2 +2x+4x+8 (x) 2 -(3) 2 /x 2 +2x+4x+8 x 2 -9/x 2 +6x+8 au~qr x 2 -9/x 2 +6x+8 au~qr

13 pirmyX ivAMjk dw rUp (x 2 -1/x-4)/ (x+5/x+4) nUM pirmyX ivAMjk dy rUp iv`c ilKo? (x 2 -1/x-4)/ (x+5/x+4) nUM pirmyX ivAMjk dy rUp iv`c ilKo? (x 2_ 1)/(X-4)X(X+4)/(X+5) (x 2_ 1)/(X-4)X(X+4)/(X+5) X 3 +4x 2 -x-4 =X 2 +5x-4x+20 X 3 +4x 2 -x-4 =X 2 +5x-4x+20 x 3 +4x 2 -x-4/x 2 +x-20 au~qr x 3 +4x 2 -x-4/x 2 +x-20 au~qr

14 AiBAws 1. hyTW iliKAW iv~coN ikhVy pirmyX ivAMjk hn? 1. 5 x 2 +3x-4/x x 2 +3x-4/x X-2/X+4 2. X-2/X+4 2. joiNVAW dw guxn&l pqw kro? X-3/x+4,x+3/x+2 X-3/x+4,x+3/x+2 3.guxwqmk au~lt ilKo? 3x/x x/x 2 -1

15 AiBAws 4.juVn Xog au~lt ilKo? 4.juVn Xog au~lt ilKo? x-2/x+4 x-2/x+4 5.joV&l pqw kro? 5.joV&l pqw kro? X-2/x+4,x+2/x+4 X-2/x+4,x+2/x+4

16 DMnvwd


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