math problems.. simplifying?

Question

could someone please help me with these simplifying questions please..

1. Simplify completely: x^2 - 4 / x^2 +5x + 6
A) x+2 / x+3
B) x+2 / x-3
C) (x+2)(x-2) / (x+6)(x+1
D) x-2 / x+3

2. Find the sum and express in simplest form
x^2 / (x^2-9) + (2x -15) / (x^2-9)

3 Solve the equation 1/x = x / 44

4. x + 1 / x + 31 = 1 / x+3

Answer 1

x² - 4 / x² + 5x + 5

(x - 2)(x + 2)
- - - - - - - - - -- =
(x + 3)(x + 2)

x + 2 cancell

x - 2
- - - -
x + 3

- - - - - - - -s-

Answer 2

1. x^2 - 4 / x^2 +5x + 6 = (x+2)(x-2) / (x+2)(x+3)
= (x-2) / (x+3)
So D

2. x^2 / (x^2-9) + (2x -15) / (x^2-9) = (x+5)(x-3) / (x+3)(x-3)
= (x+5) / (x+3)

3. 1/x = x / 44
so 44 = x^2
so x^2 = 44
so x = + or - the squareroot of 44

4. x + 1 / x + 31 = 1 / x+3
so (x+1)(x+3) = x+31
so x^2 + 4x + 3 = x + 31
so x^2 + 4x + 3 - x - 31 = 0
so x^2 + 3x - 28 = 0
so (x+7)(x-4) = 0
so x=-7, x=4

Answer 3

1. x^2-4/x^2+5x+6
First factorize the x^2-4 using formula a^2-b^2=(a+b)(a-b)
x^2-4 = (x)^2-(2)^2
=(x+2)(x-2)
Then factorize x^2+5x+6
x^2+5x+6 = (x+2)(x+3)
So , x^2-4 / x^2+5x+6 = (x+2)(x-2)/(x+2)(x+3)
Divide (x+2) and the answer is :
(x+2)(x-2)/(x+2)(x+3) = x-2 / x+3
It's D
2. x^2/x^2-9 + (2x-15)/x^2-9 = x^2+2x-15 / x^2-9
=(x+5)(x-3) / (x+3)(x-3)
Divide x-3 , and the answer is :
(x+5)(x-3) / (x+3)(x-3) = x+5/x+3

3 . 1/x=x/44
Cross Multiply !
x^2=44
x= ±√44
=±2√11
The answer could be 2√11and -2√11

4. x+1/x+31 = 1/x+3
(x+1)(x+3)=x+31
x^2+4x+3 = x+31
x^2+3x-28 = 0
Factorize it!
(x+7)(x-4) = 0
x = ( -7,4)

Answer 4

1.x^2-4/ x^2+5x+6
(x-2)(x+2)/(x+2)(x+3)

x-2/x+3

2. x^2(x^2-9) + 2x-15/x^2-9
x^2-9 is the lcd

x^2+2x-15/ (x-3)(x+3)
(x-3)(x+5)/(x-3)(x+3)

(x+5)/ (x+3)

3. 1/x=x/44
x^2=44
x=sqrt of 44= 2 x +/- sqrt of 11

4. x+1/x+31=1 /x+3

(x+1)(x+3)=x+31
x^2+4x+3=x+31
x^2+3x-28=0
(x+7)(x-4)=0
x=-7 x=4

Answer 5

(x^2-4)/(x^2+5x+6)
=[(x+2)(x-2)]/[(x+2)(x+3)]
=(x-2)/(x-3)

x^2/(x^2-9) +(2x-15)/(x^2-9)
=(x^2+2x-15)/(x^2-9)
= [(x+5)(x-3)]/[(x+3)(x-3)]
= (x+5)/(x+3)

1/x=x/44
Cross multiply to get:
x^2=44
x= +/- sqrt(44) = +/- 2sqrt(11)

(x+1)/(x+31) = 1/(x+3)
(x+1)(x+3) = x+31
x^2+4x+3 =x + 31
x^2-3x -28 = 0
(x-7)(x+4) = 0
x = 7 and x = -4

Answer 6

(x^2-4)/(x^2+5x+6)
=(x+2)(x-2)/(x+3)(x+2)
=(x-2)/(x+3) or A

x^2/(x^2-9) + (2x-15)/ x^2-9
=x^2/(x^2+2x-24) * 1 / x^2-9
=x^2 / (x^2-9)(x^2+2x-24)
=x^2/(x^4+2x^3-24x^2-9x^2-19x+216)
=x^2/(x^4+2x^3-33x^2-19x+216)

1/x = x/44
Cross multiply
1(44)=x^2
44=x^2
x=sq rt of (4*11)
x=2 sq rts of 11

x+1 / x+31 = 1/x+3
Multiply by x+3
(x+1)/(x+31)(x+3)=1
(x+1)(x+3)/x+31=1
multiply by x+31
(x+1)(x+3) = x+31
x^2+4x+3 = x+31
x^2+3x-28=0
(x+7)(x-4)=0
x=-7 or x=4

Answer 7

1. (x -2)(x+2)/(x+3)(x+2)
(x-2)/x+3
2. first simplify
x^2*(x+3)(x-3)/x^2-9+2x-15
x^2*(x+3)(x-3)/x^2+2x-24
x^2*(x+3)(x-3)/(x+6)(x-4)
Cant simplify anymore

3. x^2=44

Answer 8

Sorry .... I'm not your math tutor