Question

Simplify completely quantity 7 x squared plus 11 x minus 6 all over quantity 7 x squared minus 10 x plus 3.

Answer 1

quantity x plus 2 over quantity 7 x plus 3
quantity x plus 2 over quantity x minus 1
quantity 7 x minus 6 over quantity x minus 1
quantity 7 x minus 6 over quantity 7 x plus 3

Answer 2

7x^2 + 11x - 6
--------------
7x^2 - 10x + 3

Answer 3

Yep! Thats what it looks like

Answer 4

can you factor the 2 functions?

Answer 5

7x^2 + 11x - 6 = (7x + a)(x + b)

we need to figure out what a and b might be

Answer 6

i dont know how to factor them

Answer 7

a times b must equal -6
and a + 7b must equal 11

Answer 8

lets try the ac method
7 * 6 = -42

so we have to look at the factors of -42

Answer 9

how did you get negative by multiplying 2 positives?

Answer 10

- and keep in mind that miiddle term is + 11x

Answer 11

7*-6 sorry

Answer 12

oh ok lol

Answer 13

Oh! So ac represent 7 and -6

Answer 14

14* -3 = -42 looks promisiing because tis will give us 14 - 3 = 11

Answer 15

yea
from ax^2 + bx + c

Answer 16

so lets try
7x^2 + 14 - 3x - 6

Answer 17

factior this by grouping ( that is the first 2 and last 2 terms)

Answer 18

how did you get 14?

Answer 19

7x^2 + 14x - 3x - 6
= 7x(x + 2) - 3(x + 2)

do you follow that OK?

Answer 20

- i should have written 14x

Answer 21

typo

Answer 22

ok i follow

Answer 23

ok
now since x+ 2 is common to the 2 parts we can write

(x + 2)(7x - 3) and theses are the factors of the top part of the fraction

7x^2 - 10x + 3 can be factored in a similar fashion.

note , here ac = + 21

Answer 24

now to get -10x you need -7 and -3

so can you continue?

Answer 25

its -7 and -3 because their product is 21 and theire sum is -10

Answer 26

so 3 over 7

Answer 27

no - next its

7x^2 - 7x - 3x + 3

- now you need to factor by grouping as we did before

Answer 28

fist factor 7x^2 - 7x ( take out common factor 7x)

Answer 29

- look back at the previous post where we were at this stage

Answer 30

Im lost :/

Answer 31

divide 7x^2 by 7x then divide -7x by 7x and youll get what goes in the parenthesis

Answer 32

7x^2 - 7x = 7x(x - 1)

Answer 33

so we have

7x(x - 1) - 3x + 3

- now factor -3x - 3 ( take out 3)

Answer 34

* take out -3

Answer 35

still confused?

Answer 36

yeah

Answer 37

So many numbers

Answer 38

-3x - 3 = -3(x + 1) - understand this?

Answer 39

yes

Answer 40

-3x / -3 = x and -3/-3 = + 1

so x + 1 goes into the brackets. giving -3(x + 1)

Answer 41

ok so we have

7x(x + 1) - 3(x + 1)

- now (x +1) is common to both parts so it simplifies to
(7x - 3)(x + 1)

Answer 42

- 7x - 3 is placed in another pair of brackets

Answer 43

* 7x - 3

Answer 44

finally we are left with

(7x - 3)(x + 2)
------------
(7x - 3)(x - 1)

Answer 45

Now the 7x-3 is in top and bottom parts so it cancels out
so we are left with

(x + 2) / ( x - 1)

Answer 46

which is choice b

Answer 47

Hm. I started to understand more towards the end. I think because of the long process it confuses me. Can you help with another? It'll help me a lot, ill post it seperately of course

Answer 48

I made a mistake in calculating the second part but we got the right answer in the end

Sorry I have to go now for 30 minutes. be back later.

Answer 49

Oh okay!

Answer 50

thanks for the help

Answer 51

Yeah it is a long process and takes some practice to perfect.

Answer 52

yw