CA Algebra I: rational expression ka batwara

66-70, more simplifying of rational expressions

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Ham problem 66 pe hain

x squared minus 4x plus 4, divided by x squared

minus 3x plus 2apne lowest term mein kya hoga

ab dono quadratic equation ka factor nikal na hai

or fir dekhna hai ki factor kat te hai ya nahi

Chalo koshish karte hain.

numerator, eska batwara karna to asan lag raha hai.

Kin do anko ka multiply karke mujhe 4 milega?

Aur jab mein unhe add karun to -4 milega?

Toh -2 do hua na?

-2 aur -2, -4 hota hai.

-2 squared 4 hota hai.

To yeh x minus 2 times x minus 2 hua.

Aur agar tumhe yakeen nahi hai to.

dono factor ko Multiply karke dekhlo

divided by,kin do numbers?

Iska batwara ho sakte hain.

dono numbers ka sign same hona chahiye kyunki

tab tum enhe numberon ko multiply karte ho to tumhe positive milta hai

Yeh dono number negative honge kyunki jab tum

inhe jodo ge tab tumhe -3 milega

Chalo dekhte hain -2 aur -1.

-2 times -1, positive 2 hota hai.

-2 plus -1, -3 hota hai.

To x minus 2 times x minus 1 hua.

Agar hum ye bole ki x kabhi 2 nahi ho sakta, kyunki agar x 2 hua

to ye expression undefined ho jayega, isliey hum ise kat sakte hain.

Tum bad mein padhoge ki iski vajah se rekha-chitra mein ek ched ho jata,

kyunki vahan ye function undefined hai.

Tumhare pas -2 over -1 bacha hai.

Aur ye choice A hai.

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Saval 67( sixty seven)

Yeh acha abhyas hai.

hamare ase kai sare problem hain

veh puch te hain --- 12a cubed minus 20a

squared over 16a squared plus 8a

apne lowest terms mein kya hoga

Pehle dono( Numerator, denominator) ko bat kar dekhte hain ki kya hota hai.

To numerator mein --mujhe rang badalne do --

dono terms(12 and 20) 4 se divisible hain or a sqare se divisible hain

To 4a squared nikal lete hain.

Toh hume 4a squared milta hai.

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12 divided by 4, 3 hota hai.

Aur "a" cube divided by "a" square "a" hot hai.

Toh 12a cubed divided by 3a squared, 3a hota hai.

-20 -- mein plus minus20 bhi keh sakta hoon --

par tumhe ye samajh mein ata hai

20 divided by 4, 5 hota hai.

Aur "a" squared divided by "a" squared, keval "a" hota hai.

Aur agar tumhe yakin nahi hai to multiply karke dekh lo.

4a squared times 3a, 12a cubed(12a^3) hota hai.

Aur 4a squared(4a^2) times -5, -20a squared(-20a^2) hota hai.

Toh yeh kam karta hai.

Tum denominator karo.

Dekhte hain, yeh dono 8a se divisible hain.

To batwara kar dete hain.

16 divided by 8, 2 hota hai.

a squared(a^2) divided a, a hota hai.

To 16a squared(16a^2) divided by 8s, 2a hota hai.

Aur agar tum dosri taraf jao, to 8a guna 2a squared(2a^2)

16a squared (16a^2) hota hai.

Toh yeh bhi kam karta hain.

plus 1

8a times 1, 8a hota hai.

Dekhte hain ki hum yahan kya kar sakte hai.

Yeh ek ban jata hai.

Yeh do ban jata hai.

Aur a squrared(a^2) divided by "a", yeh 1 ban jata hai aur

yeh bas "a" ban jata hai.

Aur humare pas "a" times 3a minus 5 over 2

times 2a plus 1 bachta hai.

Aur dekhte hain.

Yeh pasand D hai.

Mujhe laga ki yeh hume phir se multiply karne ko kahenge.

Lekin pasand d iska uttar hai.

Saval adsath( sixty eight)

Oh ye wala badhiya hai.

Mein ise likh deta hoon.

Yeh chahte hain ki hum kuch guna karen.

Yeh kehte hain 7z squared( 7z^2) plus 7z -- yeh poora --

divided by 4z plus 8

times z squared(8z^2) minus 4 -- yeh poora -- divided by z cubed

plus 2z squared(2z^2) plus z equals

Tumhe lag raha hoga, hey bhagvan mujhe ye sare terms

multiply karne padenge or divide bhi karne padenge

Lekin, mere khyal mein, sabse achi cheej inhe batna

hoga aur phir saare factors

ek doosre ko kat denge

Aur yeh ek aasan sa prashn ban jayega.

dono terms(7z^2 or 7z) 7z se divisible hain

to 7z ko bahar nikal letein hain

to numerator = 7z(z+1)

to numerator = 7z(z+1)

to numerator = 7z(z+1)

to numerator = 7z(z+1)

agar tum multiply karke bracket khol dete hon to tumhe

7z squared plus 7z ( 7z^2 + 7z) milta hai

jab tum fractions multiply karte hon, to ye sirf numerator times

the numerator ,over denominator times the

denominator hota hai

to 7z(z+1) times the numerator

z squared minus 4 (z^2-4), jo ki (a^2-b^2) ke form mein hai

to z^2-4 = (z-2)(z+2)

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to z^2-4 = (z-2)(z+2) , asha karta hoon

tumhe ye pahchan pa rahe ho es samhe par

ab denominator pe dhyan deten hain

4 ko bahar nikal lete hain, to yeh 4 times (z+2) ho jata hai.

8 divided by 4 is 2 times -- ham z ko bahar nikal sakte

hai edhar, to hamhe z(z^2+2z+1) milta hai

mujhe lagta ab kam pura hona vala hai

ab hamhe (z^2+2z+1) ko factor karna hai

abhi mein sab vapas likh deta hoon

to ye barbar hai 7z(z+1)(z+2)(z+6)

to ye barbar hai 7z(z+1)(z+2)(z+6)

divided by 4(z+2)(z)( aur ye kya hai)

divided by 4(z+2)(z)( aur ye kya hai?)

divided by 4(z+2)(z){ ye (z+1)^2 ke barabar hai}

(z+1)(z+1), 1 times 1, 1 hota hai

or 1+1 , 2 hota hai

so time (z+1)(z+1)

or ab maza aayega

ye edhar 1hai, or ye bracket hai.

or ab ham sab cancel out karna chalunn kartein hain

or ham ye man letein hain ki denominator kabhi zero ke

barabar nahi hoga

ab dekhtein hain, ye (z+2)

es (z+2) ko cancel out kardega

Ye (z+1) en mein se koi (z+1) ko cancel out kar dega

mein esse cancel kar deta hoon

ye 'z' es 'z' ko cancel out kardega

or ab hamare pas kya bachta hai

sab ab simplify ho gaya hai 7(z-6) over

4(z+1) mein

ha ha

oh maine edhar (z-b) likh diya

ye to (z+2)(z-2) hai

vo sab (a^2-b^2) = (a-b)(a+b) mein maine galti kar di

(z^2-4) = (z+2)(z-2) hot hai

na ki z-b, mujhe laga ye 6 tha

to yeh (z-2) hai

or yeh (z-2) hai

to sahi choice 1 hai

galti ke liye sorry

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ok, vo ab chahatein ki ab ham ye sab vapas karein

vo ab chahatein ki ab ham product find karein (x+5) over (3x+2)

times (2x-3) over (x-5)

yahan pe ham jyada kuch simplification nahi kar saktein hain

hamein bas multiply karna hoga

to ye barabar hoga (x+5)(2x-3)

divided by 3x

mein bas numerator ko multiply kar raha hoon or fir

denominator ko multiply kar raha hoon -- ( 3x+2)(x-5)

or ham ab dono binomial ko multiply kar dete hain,

x*2x = 2x^2

x*(-3) = -3x

5*2x=10x

5*(-3)=(-15)

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ab ham denominator ko multiply karte hain

3x*x = 3x^2

3x*(-5) = 15x

2*x = 2x

2*(-5)=(-10)

or ab dektein hain ki ham simplify kar saktein hai ya nahi

numerator ko dekho 2x^2

-3x+10x

to ye 7x -15 hua

ye sab over 3x^2

-15x + 2x

13x - 10 hua

or ye choice hua D vala

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Agla saval

Problem 70

vo chahte hain ham

practise kartein rahein

to vo liktein hai x^2+8x+16,over x+3

divided by 2x plus 8, over x squared minus 9

to jab tum ek fraction se divide karte hai

to tum us fraction ke inverse se multiply kar dete ho

to ye barabar hai x squared plus 8x plus + sixteen (x^2+8x+16) over x plus three (x+3)

time eska ulta(inverse), x squared minus nine (x^2-9)

over 2x plus eight (2x+8)

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chalo ab ese ham simplify kartein hain

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to ye ,4 plus 4 is 8 hai, or ye 4 times 4 is 16 hai.

to ham ese ase likh saktein hai x plus 4 times x plus 4.....(x+4)(x+4)

to ham ese ase likh saktein hai x plus 4 times x plus 4.....(x+4)(x+4)

x squared minus 9... a squared minus b squared.. (a^2-b^2) ke form mein hai

to ye hua (x+3)(x-3)...x plus 3 times x minus 3

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ham edhar 2 bahar nikal saktein hai. to ye ban jayega

2(x+4) .. 2 times x plus 4

hamare par edhar x+3 hai

or han jab ham fractions multiply kartein hain ham bhas

sare numerators ko multiply kar dete hain over sare denominators ko multiply kar dete hai

to tum edhar ek line bana dete ho

to numerator (x+4)(x+4)(x+3)(x-3)...x plus 4 times x plus 4 times x plus 3 times x minus 3 hua

to numerator (x+4)(x+4)(x+3)(x-3)...x plus 4 times x plus 4 times x plus 3 times x minus 3 hua

ye sab divided by (x+3)(2x+4)..x plus 3 times 2 times x plus 4

to ab thodi cancellation kartein hain

ye hi to maze vali bat hai

to hamarein pas (x+4) or (x+4) hai, enhe cancel kardo

to hamarein pas (x+4) or (x+4) hai, enhe cancel kardo

hamarein pas (x+3) or (x+3) hai, enhe bhi cancel kar do

hamarein pas (x+3) or (x+3) hai, enhe bhi cancel kar do

or ab hamarein pas kya bachta hai

hamarein pas bachta hai (x+4)(x-3)

ye sab divided by 2

or choice C vala hai

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