Question

Find all values of $x$ such that
\[\frac{2x}{x + 2} = -\frac{6}{x + 4}.\]

Answer 1

Answer:x_1= -1 or x_2= -6

Step-by-step explanation:

In the pictures

Answer 2

By using factorization, $\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\]$ , values of x are -2, 3.

What is factorization?

Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number.

These numbers are broken down into factors or divisors.

For an integer, factorization is decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number and these composing integers are called factors of that considered integers.

Given

$\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\]$

Cross multiplication;

2x(x + 4) = 6(x + 2)

$2x^{2} + 8x = 6x + 12\\\\2x^{2} + 8x - 6x - 12 = 0\\\\2x^{2} + 2x - 12 = 0\\\\x^{2} + x - 6 = 0$

Divide above equation by 2, we get

$x^{2} + x - 6 = 0$

(x +2) (x-3)

x = -2, 3

Therefore, By using factorization, $\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\]$ , values of x are -2, 3.

Find out more information about factorization here;

brainly.com/question/1863222

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