Need some help... Stuck on a couple problems....?

Question

1. Write in simplest form:
x^2 - 6x + 9 / (over) x - 3

2. Subtract. Write your answer in simplest form:
9 / (over) y - 7 minus 1 / (over) y + 1

Answer 1

Let me restate the problems I'm solving:
1. [x²-6x+9] / [x-3]

2. [9] / [y-7] - [1] / [y+1]


Answers:


1. Factor the Numerator x² - 6x + 9 into (x-3)(x-3) to get:

[x² - 6x + 9] / [x-3] = [(x-3)(x-3)] / (x-3)

then cancel an x-3 out of both the numerator and the denominator to get the answer:

(x - 3); x not equal to 3

this last part is necessary because the original expression causes the denominator to go to zero when x = 3. Thus at this point, the original expression is undefinied and therefore the reduced (answer) form is also not allowed to exist.



2. If we multiply the first fraction by [y+1] / [y+1] and the second fraction by [y-7] / [y-7] we get a common denominator and can then do the subtraction:

[(9)(y+1) - (1)(y-7)] / [(y-7)(y+1)] which reduces to:

[9y + 9 - y + 7] / [(y-7)(y+1)]

[8y + 16] / [(y-7)(y+1)]

[8 (y+2)] / [(y-7)(y+1)]

Answer 2

(x^2 - 6x + 9) / (x - 3) =
((x - 3)(x - 3))/(x - 3) =
x-3

9/(y - 7) -1/(y + 1) =
9(y+1)/((y - 7)(y + 1)) - (y - 7)/((y + 1)(y - 7)) =
(9(y + 1) - (y - 7))/((y - 7)(y + 1)) =
(9y + 9 - y + 7)/((y - 7)(y + 1)) =
(8y + 16)/((y - 7)(y + 1)) =
8(y + 2)/(y^2 + y - 7y - 7) =
8(y + 2)/(y^2 -6y - 7)

Answer 3

(1) Factor:

x^2 - 6x + 9 = (x - 3)(x - 3)

[(x - 3)(x - 3)] / (x - 3) = x - 3

(2) 9/y - [(7 - 1) / (y + 1)]
9/y - 6/(y + 1)
9(y + 1) / (y(y + 1)) - 6y / (y(y + 1))
[9y - 6y + 1] / [y(y + 1)]
(3y + 1) / (y(y + 1))

Answer 4

1. factorise x^2 -6x +9 = (x-3)(x-3)
when you divide the result by (x-3), you get

(x-3)(x-3)/(x-3) = (x-3). ANS

Answer 5

1) x-3
2) question not clear but i think thats what you mean?

[(9/y) - 7] - [1/(y+1)]

answer: (y+9-7y^2) / (y^2+y)

Answer 6

x² - 6x + 9
- - - - - - - -.=
X - 3

- - - - - - - -

Factor the numerator

x² - 6x + 9 = 0

x² - 3x - 3x + 9 = 0

x(x - 3) - 3(x - 3) = 0

(x - 3)(x - 3)

- - - - - - - - - -

(x - 3)(x - 3)
- - - - - - - - -.=
x - 3

x - 3
- - - - - -.=
1

x - 3

- - - - - - - -s-