Rearranging to make x the subject so i can solve

[toodey]

Homework Statement

Square root over all in brackets (x+2)/(x-2)=1/2

Homework Equations

REARRANGING

The Attempt at a Solution

-0.33? but need to show my working but used my calculator, i don't no how to get the x's to become one

 

[CompuChip]

Is it
$$\sqrt{\frac{x + 2}{x - 2}} = \frac12$$
or
$$\frac{\sqrt{x + 2}}{x - 2}} = \frac12?$$

Anyway, first you want to get rid of the square root, then of the fraction and finally you will get a quadratic equation which you can solve.

 

[nlightner]

To solve for x, we can rearrange the equation to isolate x on one side. First, we can multiply both sides by (x-2) to get rid of the denominator on the left side. This gives us:

√(x+2) = 1/2 * (x-2)

Next, we can square both sides to eliminate the square root on the left side. This gives us:

((x+2) = 1/4 * (x-2)^2

Expanding the right side gives us:

x+2 = 1/4 * (x^2 - 4x + 4)

Multiplying both sides by 4 to eliminate the fraction gives us:

4x+8 = x^2 - 4x + 4

Moving all terms to one side gives us:

x^2 - 8x - 4 = 0

Using the quadratic formula, we can solve for x:

x = (8 ± √(8^2 - 4 * 1 * (-4))) / 2

x = (8 ± √(64 + 16)) / 2

x = (8 ± √80) / 2

x = (8 ± 8.94) / 2

x = 4.47 or -0.47

So, the solutions for x are 4.47 and -0.47.