Please help me with this math?

Question

Quadratic Equation
Show me how you figure this out please

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

Answer 1

(x+2)/(x²-2) = (2)/(3-x)
Cross multiply
(x+2)(3-x) = 2(x^2-2)
So -x² - x + 6 = 2x² -4
So 0 = 3x² + x - 10

Looking for two numbers whose sum = +1 (ie b) and product = 3 * -10 = 30 (ie a*c)
These numbers are +6 and - 5
So + x = + 6x - 5x.
So 3x² + 6x - 5x - 10 = 0

3x(x + 2) - 5( x + 2) = 0
(3x - 5)(x + 2) = 0
Thus x = -2 or 5/3

Answer 2

remember a/b = c/d equals to ad = bc

so (x+2) (3-x) = 2 (x^2-2) make the multiplications

3x-x^2+6 -2x = 2x^2 -4
x-x^2+6 = 2x^2-4
-3x^2 +x +10 = 0 or if you change the signs

3x2-x -9 =0

Answer 3

proportional Problem

Multiply the means

Multiply the extremes

(x + 2) / (x² - 2) = 2 / 3 - 4

The means = 2(x² - 2)

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

The means = 2x² - 4

The extremes = (x + 2)(3 - x)= 3x + 6 - x² - 2x = -x² +x + 6

2x² - 4 = - x² + x + 6

2x² - 4 + x² = - x² + x + 6 + x²

3x² - 4 = x + 6

3x² - 4 - x = x + 6 - 6

3x² - x - 4 = 6

3x² - x - 4 - 6 = 6 - 6

3x² - x - 10 = 0

- - - - - -s-

Answer 4

(x+2)/(x^2-2) = (2)/(3-x)
(x+2)(3-x) = 2(x^2-2) <<<<<<< cross-multiplication
-x^2 + x + 6 = 2x^2 - 4
-3x^2 + x + 10 = 0
(3x+5)(-x+2) = 0

x = {-5/3, 2}

Answer 5

first cross mulitply 2(2x-2) = (x+2)(3-x)

open brackets 4x -4 = 3x+6-x(square) - 2x

move all to 1 side to get equations 4x-3x+2x -4 -6 +x(square) = 0

to get x(square) + 3x -10 =0

factorise (x+5)(x-2) = 0

therefore x = -5 or 2

Answer 6

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

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

3x + 6 - x^2 - 2x = 2x^2 - 4

-2x^2 - x^2 + 3x + 6 - 2x = -4

-3x^2 + x + 6 = -4

-3x^2 + x + 10 = 0

Use standard function: (ABC)

x =( (-b) (+-) sqrt(b^2-4ac) ) / (2a)

x = -(5/3) and x = 2

Hopefully this makes sense....

Answer 7

rearranging we get 3x^2-x-10=0
or (3x+5)(x-2)=0
so x=-5/3 or 2

Answer 8

(x+2)(3-x)=2(x^2-2)
3x-x^2+6-2x=2x^2-4
x-x^2-2x^2+6+4=0
x-3x^2+10=0
-3x^2+x+10=0
3x^2-x-10=0
(x-2)(3x+5)=0
x=2 or x=-5/3 (solved)

Answer 9

im too lazy to do it but here is the formula just substitute the values in....

x=(-(b) plus and minus( square root of b square minus 4 x A x C))
dvided by 2
x= answer