What is the simplified form of x plus 1 over x squared plus x minus 6 ÷ x squared plus 5x plus 4 over x plus 4 ?
1 over the quantity x plus 3 times the quantity x plus 4
1 over the quantity x plus 3 times the quantity x minus 2
1 over the quantity x plus 4 times the quantity x minus 2
1 over the quantity x plus 3 times the quantity x plus 1

- anonymous

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- anonymous

@satellite73

- anonymous

\[\frac{ x + 1 }{ x^2 + x -6 } \div \frac{ x^2 + 5x + 4 }{ x + 4 }\]
@satellite73

- anonymous

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## More answers

- anonymous

http://www.wolframalpha.com/input/?i=%28x%2B1%29%2F%28x^2%2Bx-6%29*%28x%2B4%29%2F%28x^2%2B5x%2B4%29

- anonymous

you go that right?

- anonymous

nice use of the equation tool btw

- anonymous

i can show you another trick in using wolfram

- anonymous

okay and heres the question

- anonymous

simplify (12z^2 - 25z + 12)/ (3z^2 + 2z - 8)

- anonymous

using the link i got (4z - 3)/(x + 2)

- anonymous

ok i so take what you wrote, copy and paste it directly in to wolfram

- anonymous

yeah i did that and got (4z - 3)/(x + 2)

- anonymous

yeah i get that too, but of course with a z

- anonymous

i could also show you how to do it without wolfram, it is "factor and cancel"

- anonymous

oh yeah typo lol sorry okay i think it'll be better without wolframe alpha in case my teacher asks

- anonymous

ok then here is the deal
do you know how to factor?

- anonymous

sometimes but not really it'll be helpful if you showed me though

- anonymous

i don't actually, believe it or not if i wanted to factor i would cheat

- anonymous

what i mean is that i have no good way to show you how

- anonymous

i usually use a site for factoring

- anonymous

that works, of course wolfram will do that too

- anonymous

so in case the teacher asks, you can say something like this ;

- anonymous

\[ (12z^2 - 25z + 12)=(4 z-3) (3 z-4)\] and
\[(3z^2 + 2z - 8)=
(3 z-4) (z+2)\]

- anonymous

so
\[\frac{12z^2+25z+12}{3z^2+2z-8}=\frac{4z-3)(3z-4)}{(3z-4)(z+2)}\]

- anonymous

oh and then you cross out (3z - 4)?

- anonymous

there is a common factor top and bottom of \(3z-4\) which cancels, you get
\[\frac{(4z-3)(3z-4)}{(3z-4)(z+2)}=\frac{4z-3}{z+2}\]

- anonymous

exactly what you said

- anonymous

that is the idea of all of these
factor and cancel

- anonymous

okay cool i get it now

- anonymous

as to how to factor, you are pretty much on your own, but you can use wolfram to do it for sure

- anonymous

okay thnx

- anonymous

and you can use wolfram to give the final answer too, but once you have it factored it is easy to cancel

- anonymous

ill also ask someone else on os

- anonymous

want to try another one ?

- anonymous

yeah

- anonymous

ok i get a cup of coffee, you post

- anonymous

ok What polynomial identity should be used to prove that 21 = 25 - 4?

- anonymous

wow do you have any choices? \(21=25-4\) is simple arithmetic

- anonymous

What polynomial identity should be used to prove that 21 = 25 - 4?
Difference of Cubes
Difference of Squares
Square of Binomial
Sum of Cubes

- anonymous

ooh ok

- anonymous

25 and 4 are two squares

- anonymous

then B?

- anonymous

\[25=5^2\] and \[2^2\] so yeah B

- anonymous

what a dumb retricequestion
next?

- anonymous

thnx

- anonymous

given the parent function of f(x) = x3, what change will occur when the function is changed to f(x - 3)?
Shift to the right 3 units
Shift to the left 3 units
Shift up 3 units
Shift down 3 units

- anonymous

when you subtract inside the function it move is 3 units to the RIGHT

- anonymous

thnx

- anonymous

ased on the table of values below, find the slope between points where x = 1 and where x = 4.
x y
1 8
3 6
4 −1

- anonymous

what is the corresponding y value when x = 1?

- anonymous

ok ok

- anonymous

8

- anonymous

\[\frac{-1-8}{4-1}\] is whatyou have to compuote

- anonymous

i get
\[\frac{-9}{3}=-3\]

- anonymous

thnx

- anonymous

yw

- anonymous

how many more?

- anonymous

a couple
Which of the following expressions is the conjugate of a complex number with 2 as the real part and 3i as the imaginary part?
2 + 3i
2 − 3i
3i + 2
3i − 2

- anonymous

the conjugate of \(a+bi\) is \(a-bi\)

- anonymous

so b?

- anonymous

the conjugate of \(2+3i\) is \(2-3i\) that was an easy one

- anonymous

yeah b

- anonymous

okay thnx

- anonymous

yw next?

- anonymous

Two car washers, Michelle and Nancy, are working on your car. Michelle can complete the work in 6 hours, while Nancy can complete the work in 3 hours. How many hours does the car washing take if they work together?
3
2
six eighths
four thirds

- anonymous

we go right to the answer (otherwise it take like forever) but remember this simple trick
\[\frac{6\times 3}{6+3}\]

- anonymous

got that ?

- anonymous

so 18/9 = 2

- anonymous

yes

- anonymous

Bob and Susie wash cars for extra money over the summer. Bob's income is determined by f(x) = 6x + 13, where x is the number of hours. Susie's income is g(x) = 4x + 18. If Bob and Susie were to combine their efforts, their income would be h(x) = f(x) + g(x). Assume Bob works 3 hours. Create the function h(x) and indicate if Bob will make more money working alone or by teaming with Susie.
h(x) = 2x + 5, work alone
h(x) = 2x + 5, team with Susie
h(x) = 10x + 31, team with Susie
h(x) = 10x + 31, work alone

- anonymous

see the trick? it is easy

- anonymous

yup

- anonymous

\[g(x) = 4x + 18\]
\[h(x)=6x+13\]
\[g(x)+h(x)=4x+18+6x+13\]

- anonymous

combine like terms,what do you get?

- anonymous

10x + 31

- anonymous

ok good so C or D

- anonymous

yup but i think its with team work so C?

- anonymous

not sure
if bob works 3 hours alone he makes
\[f(3)=6\times 3+13=18+13=31\]

- anonymous

oh so D

- anonymous

don't jump the gun

- anonymous

if they both work 3 hours they make a total of
\pg(3)=10\times 3+31=61\]

- anonymous

oh

- anonymous

\[h(3)=10\times 3+31=61\]\]

- anonymous

if he has to split it, then yes he is better off working alone

- anonymous

so is its C then?

- anonymous

i think D
not really clear, but i think D

- anonymous

ok

- anonymous

next?

- anonymous

What is the equation of the quadratic graph with a focus of (3, 6) and a directrix of y = 4?

- anonymous

this takes a second

- anonymous

k

- anonymous

half way between 6 and 4 is 5, so the vertex is \((3,5)\)

- anonymous

therefore it will look like
\[4p(y-5)=(x-3)^2\] we need \(p\)

- anonymous

the distance between 4 and 5 is 1, so p = 1 and one answer is
\[4(y-5)=(x-3)^2\]
now sure what your answer choices look like

- anonymous

f(x) = one fourth (x − 3)2 + 1
f(x) = one fourth (x − 3)2 + 5
f(x) = −one fourth (x − 2)2 + 5
f(x) = −one fourth (x − 2)2

- anonymous

\[4(y-5)=(x-3)^2\\
y-5=\frac{1}{4}(x-3)^2\\
y=\frac{1}{4}(x-3)^2+5\]

- anonymous

thnx
Which of the following is a solution of x2 + 2x + 8?
4 + i times the square root of 7
−1 + i times the square root of 7
2 + i times the square root of 7
−4 + i times the square root of 7

- anonymous

x^2 + 2x +8

- anonymous

you want do step by step? or wolfram it?

- anonymous

step by step so i can learn

- anonymous

ok
a) subtract 8 from both sides, what do you get?

- anonymous

if that is not clear say so i will tell you

- anonymous

oh note that you are starting with
\[x^2+2x+8=0\]

- anonymous

x^2 + 2x = 8

- anonymous

i meaN -8

- anonymous

ok good

- anonymous

SO X^2 + 2X = -8

- anonymous

\[x^2+2x=8\] now what is half of 2?`

- anonymous

oops
\[x^2+2x=-8\] what is half of two?

- anonymous

1

- anonymous

so x^2 + x = -8/2?

- anonymous

no slow

- anonymous

oh sorry

- anonymous

half of 2 is 1, so we go right to
\[(x+1)^2=-8+1^2\] or \[(x+1)^2=-7\]

- anonymous

ok

- anonymous

take the square root, get
\[x+1=\pm\sqrt{-7}\] or
\[x+1=\pm\sqrt{7}i\]

- anonymous

subtract 1, get
\[x=-1\pm\sqrt{7}i\]

- anonymous

thnx

- anonymous

What are the possible numbers of positive, negative, and complex zeros of f(x) = -3x4 - 5x3 - x2 - 8x + 4?
Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
Positive: 1; negative: 3 or 1; complex: 2 or 0
Positive: 3 or 1; negative: 1; complex: 2 or 0
Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0

- anonymous

ok we do this, then i gotta split

- anonymous

\[f f(x) = -3x^4 - 5x^3 - x^2 - 8x + 4\]

- anonymous

it is a polynomial of degree 4, so it has 4 zeros for sure

- anonymous

there is one change in sign of the coefficients, which is a fancy way of saying that the go "minus, minus, minus, minus , PLUS" only once change in sign
therefore there is one positive zero
there cannot be no positive zeros because you count down by twos

- anonymous

\[f(x) = -3x^4 - 5x^3 - x^2 - 8x + 4\]
\[f(-x) = -3x^4 + 5x^3 - x^2 + 8x + 4\]

- anonymous

here there are 3 changes in sign
from -3 to +5, from +5 to -1 and from -1 tp +8
so there are either 3 negative zeros, or one negative zero

- anonymous

possibilities therefore are
1 positive, 3 negative (total of 4) or
1 positive, 1 negative 2 complex (total of 4)

- anonymous

now i really have to bolt
ask your sister how to do the rest
good luck!

- anonymous

thnx and ok bye

- anonymous

bye !

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