# Solve for x. a=`sqrt((x+c)/(x-c))` Please explain how you arrive at the answer.Thanks

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Expert Answers

lemjay | Certified Educator

`a=sqrt((x+c)/(x-c))`

First, eliminate the radical. So, take the square of both sides of the equation.

`a^2=(sqrt((x+c)/(x-c)))^2`

`a^2=(x+c)/(x-c)`

Then, remove the x in the denominator. To do so, multiply the equation by x-c.

`(x-c)*a^2=(x+c)/(x-c)*(x-c)`

`a^2x-a^2c=x+c`

Next, bring together the terms with x on one side of the equation. So, subtract both sides by x.

`a^2x-a^2c-x=x-x+c`

`a^2x-x-a^2c=c`

Also, add both sides by a^2c to bring together the terms without x on the other side of the equation.

`a^2x-x+a^2c-a^2c=a^2c+c`

`a^2x-x=a^2c+c`

Then, factor out the GCF at the left side.

`x(a^2-1)=a^2c+c`

And to have x only at the left, divide both sides by a^2-1.

`(x(a^2-1))/(a^2-1)=(a^2c+c)/(a^2-1)`

`x=(a^2c+c)/(a^2-1)`

**Hence, `x=(a^2c+c)/(a^2-1)` .**