solve the equation

To solve the equation, we need to isolate the variable x.

-2/x + 4 = 4/x + 3

First, let's combine the terms with x on the right side:

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

Next, multiply both sides by x to eliminate the denominator:

-6 = 3x

Now, divide both sides by 3 to solve for x:

x = -2

Therefore, the solution to the equation is x = -2.

check the solution

Let's substitute the value of x = -2 back into the original equation and see if it holds true:

-2 / x + 4 = 4 / x + 3

-2 / (-2) + 4 = 4 / (-2) + 3

-2 / (-2) = -2 = 4 / -2 + 3

1 + 4 = -2 + 3

5 = 1

Since the equation did not hold true when we substituted x = -2 back into the original equation, it indicates that x = -2 is not the correct solution for the given equation. Let's try to solve the equation again:

Given equation: -2 / x + 4 = 4 / x + 3

Multiply the entire equation by x to eliminate the denominators:

-2 + 4x = 4 + 3x

Rearrange the terms:

4x - 3x = 4 + 2

x = 6

Therefore, the correct solution to the equation is x = 6.