how do you solve this rational equation?.........?

Question

- (4/x^2+2x)=1/2x+4.....steps if possible...thanks in advance!!!!...

Answer 1

ok .. to start off.
cross multiply
so u hvae
-4(2x +4 ) = 1(x^2 +2x)
so u have
-8x - 16 = x^2 + 2x
get everything on one side and now u have a quadratic equation
0 = x^2 + 10x + 16
factor it.
(x+2)(x+8)
so u have x = -2 and x = -8
by zero product rule.

Answer 2

Read this as:-
- 4 / (x² + 2x) = 1 / 2.(x + 2)
- 4 / (x.(x + 2)) = 1 / (2.(x + 2))
- 4 / x = 1 / 2
x = - 8

Answer 3

- (4/(x^2+2x))=1/(2x+4)
- 4(2)(x + 2) = x(x + 2)
x(x + 2) + 8(x + 2) = 0
(x + 8)(x + 2) = 0
x = - 2, - 8

Answer 4

Distribute the negative sign into the first part of the eq, making:
-4x/(-x² - 2x) = (1/2)x +4
Multiply the first denomination on both sides:
-4x = ((1/2)x + 4)(-x² - 2x)
Which means: -4x = -0.5(x^3) - x² - 4x² - 8x
Which means: -4x = (x)( -0.5x² - x - 4x - 8)
divide both sides by x:
-4 = -0.5x² - 3x - 8
Which means:
0 = -0.5x² - 3x - 4
Use the quadratic formula:
X = (3 +/- √(-3² - 4(-.5)(-4)))/2(0.5)
Which means:
3 +/- √(9 - 8)
Which means 3 +/- 1
Which means: 2 or 4.
=)