Question

Can someone help me? I've been on this for awhile and it's driving me nuts.

Answer 1

x = 0, x = -2

Explanation:

We are given that the two fractions are equal. Similarly to proportions, we can multiply the "means" and "extremes," and then set them equal to each other. For example,

`(a)/(b) = (c)/(d) =\\ad=cd`

Let's do this with the given algebraic fractions.

`(2x)/(2x+4) = (3x)/(x+2) =\\ 2x(x+2) = 3x(2x+4) =\\2x^2+4x=6x^2+12x\\`

Now that we've simplified the products, let's operate on the like terms.

`2x^2+4x=6x^2+12x=\\4x^2+8x = 0`

Take these two terms and factor out their greatest common factor.

`4x^2+8x= 0 =\\4x(x+2) = 0`

When two things are being multiplied, and the product is zero, it must mean that at least one of the factors equals zero (since zero times any number equals zero). Let's set each factor equal to zero.

`4x = 0 =\\x = 0`

So, one of our answers is x = 0.

`x+2=0 =\\x = -2`

Our other answer is x = -2.

So, the answer is x = 0 and x = -2.