Question

-2 x+4
----- = ------
x+2 x^2-4

Answer 1

A. x=0, -2
B. x=0,2,-2
C.x=2,-2
D.x=0

Answer 2

A. x=0, -2

Answer 3

Solve for x over the real numbers:
-2/(x+2) = (x+4)/(x^2-4)
Multiply both sides by a polynomial to clear fractions.
Cross multiply:
-2 (x^2-4) = (x+2) (x+4)
Write the quadratic polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
8-2 x^2 = (x+2) (x+4)
Write the quadratic polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
8-2 x^2 = x^2+6 x+8
Move everything to the left hand side.
Subtract x^2+6 x+8 from both sides:
-6 x-3 x^2 = 0
Factor the left hand side.
Factor x and constant terms from the left hand side:
-3 x (x+2) = 0
Divide both sides by a constant to simplify the equation.
Divide both sides by -3:
x (x+2) = 0
Solve each term in the product separately.
Split into two equations:
x = 0 or x+2 = 0
Look at the second equation: Solve for x.
Subtract 2 from both sides:
x = 0 or x = -2
Now test that these solutions are correct by substituting into the original equation.
Check the solution x = -2.
-2/(x+2) => -2/(2-2) = infinity^~ ~~ infinity^~
(x+4)/(x^2-4) => (4-2)/(4-4) = infinity^~ ~~ infinity^~:
So this solution is incorrect
Check the solution x = 0.
-2/(x+2) => -2/(2+0) = -1
(x+4)/(x^2-4) => (4+0)/(0-4) = -1:
So this solution is correct
Gather any correct solutions.
The solution is:
Answer: x = 0

Answer 4

(x+2)*(x+4)=(x^2-4)*(-2)
x^2+4x+2x+8=-2x^2+8
3x^2+6x=0
delta=6^2-4*3*0=36
x1,2=[-6+-sqrt(delta)]/6
so x1=0
and x2=-2
so A is the correct answer