Question

How to simplify 9x^2+30x+25 / 3x+15 ? Especially how to simplify 9x^2+30x+25???

Answer 1

you could use the quadratic formula for that numerator, to factorise it, and hopefully one of the factors will cancel

Answer 2

\[ax^2+bx+c=0\]
\[x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
\[(x-x_1)(x-x_2)=0\]

Answer 3

Factor out a 3 first from the numerator and denominator.

Answer 4

thnx Use quadratic make sense.. I dont think we can factor all by 3 (25 doesnt factor 3).....

Answer 5

well you know.... 25/3....:P Jk. you're right.

Answer 6

hehe thats ok! :P

Answer 7

using quadratic equation: it looks like -30+sqrt(o) / 18 ????

Answer 8

yes, good stuff, can you simplify further

Answer 9

yes, -5/3???

Answer 10

very good.,

so now you have
\[x_{1,2}=-5/3\]
what does that look like in this form
\[(x-x_1)(x-x_2)=0\]

Answer 11

I am stuck from here..

Answer 12

http://www.sketchtoy.com/42750753

Answer 13

An alternative.

Answer 14

well we are almost there

Answer 15

is it (x+5/3) and (x-5/3) ??

Answer 16

there should be no minus sign

Answer 17

(the factors are the same)

Answer 18

\[\large a^2 +b^2 = (a+b)(a+b) = a^2 +2ab+b^2\]

Answer 19

\[\huge a^2 +b^2 = (a+b)(a+b) = a^2 +2ab+b^2\]

Answer 20

what?

Answer 21

\(\large 9x^2 +30x+25\) is a perfect square... \[\large a^2= 9x^2 \ \therefore \ a = 3x\]\[\large b^2 = 25 \ \therefore \ b = 5\]putting this into our formula, \(\large (a+b)(a+b)\) we have \((3x+5)(3x+5)\) or \((3x+5)^2\)

Answer 22

gotcha! make sense !

Answer 23

I was just elaborating what @UnkleRhaukus mentioned earlier....of breaking apart the numerator. He'll continue :P I just thought you could see some other methods.

Answer 24

ooo you made a therefore symbol :O

Answer 25

you are learning new latex symbols

Answer 26

THnx but I still dont get how to find from here.. (what UnkleRhaukus ) suggest
so now you have
x1,2=−5/3

what does that look like in this form
(x−x1)(x−x2)=0

Answer 27

x1,2=−5/3


(x+5/3)(x+5/3)=0
(x+5/3)^2 =0

Answer 28

now multiply both sides of the equation by nine

Answer 29

(9x+5)^2 for the numerator

Answer 30

not quite

Answer 31

the nine becomes a three under the ^2

Answer 32

9(x+5/3) = (9x+5) so since it is (x+5/3)^2= (9x+5)(9x+5)???

Answer 33

oh so (3x+5)^2

Answer 34

\[(x+5/3)^2 =0\\
9\times(x+5/3)^2 =9\times0\\
3^2\times(x+5/3)^2 =0\\
(3\times (x+ 5/3))^2=0\\
(3\times x+3\times 5/3)^2=0\]

Answer 35

yes

Answer 36

so the result of this equation is (3x+5)^2 / (3x+5) = (3x+5) ..Is that it???

Answer 37

i thought it was it (9x^2+30x+25) / (3x+15) = (3x+5)^2 / (3x+15)

Answer 38

does the denominator have +15 or +5?

Answer 39

darn it!!!!!.. it +5 sry..

Answer 40

oh well that is good really

Answer 41

k.. then thank you!!

Answer 42

(3x+5)^2 / (3x+5) = (3x+5) \(\huge\color{red}\checkmark \)

Answer 43

@Jhannybean , @dan815 \[\large \color{red}{(a +b)^2} = (a+b)(a+b) = a^2 +2ab+b^2\\
\large\color{red}{a^2 -b^2=(a+b)(a-b)=a^2-ab+ba-b^2}\\
\large\color{brown}{a^2 +b^2=(a-ib)(a+ib)=a^2+aib-iba+b^2}\]

Answer 44

thats really helps!!

Answer 45

\[\large \color{navy}{(a +b)^2 =(a+b)(a+b) = a^2 +2ab+b^2}\\\]
\[\large\color{blue}{a^2 -b^2=(a+b)(a-b)=a^2-ab+ba-b^2}\\\]
\[\large\color{skyblue}{a^2 +b^2=(a-ib)(a+ib)=a^2+aib-iba+b^2}\]

Answer 46

they shud have some crazy crayola color names put in too

Answer 47

red mountain glaze

Answer 48

you can use hex colours

http://openstudy.com/study#/updates/51b0e7f9e4b05b167ed2e8fe

Answer 49

Ahh... Then I was wrong.