Rearranging to make x the subject so i can solve

[toodey]

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

NEED HELP WITH MY REARRANGING, THANKS

 

[symbolipoint]

Clear the fractions; multiply left and right hand sides of the equation by 2(x-2).

 

[Architeuthis Dux]

Sure, I'd be happy to help you with rearranging the equation to solve for x. First, let's start by isolating the square root term on one side of the equation. We can do this by multiplying both sides by the denominator of the fraction, which in this case is (x-2).

(x-2) * square root((x+2)/(x-2)) = (x-2) * 1/2

Next, we can simplify the left side by canceling out the (x-2) terms, leaving us with just the square root of (x+2).

square root(x+2) = (x-2)/2

To get rid of the square root, we need to square both sides of the equation.

(square root(x+2))^2 = ((x-2)/2)^2

This gives us:

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

Now, we can expand the right side by multiplying (x-2)^2, which gives us:

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

To simplify the right side, we can divide each term by 4.

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

Finally, we can move all terms to one side and set it equal to 0.

x^2/4-x+1-2 = 0
x^2/4-x-1 = 0

Now, we can solve for x using the quadratic formula or by factoring. I'll use the quadratic formula in this case.

x = (-b ± √(b^2-4ac)) / 2a

Plugging in our values for a, b, and c, we get:

x = (-(-1) ± √((-1)^2 - 4(1)(-1))) / 2(1)
x = (1 ± √(1+4)) / 2
x = (1 ± √5) / 2

Therefore, the two possible solutions for x are:

x = (1+√5)/2 or x = (1-√5)/2

I hope this helps you in solving the equation and finding