√9+x - √x=5/√9+x

√9 + x - √x = 5 / √9 + x

3 + x - √x = 5 / 3 + x ( becouse √9 = 3 )

Subtract x to both sides

3 + x - √x - x = 5 / 3 + x - x

3 - √x = 5 / 3

Subtract 3 to both sides

3 - √x - 3 = 5 / 3 - 3

- √x = 5 / 3 - 3

- √x = 5 / 3 - 9 / 3

- √x = - 4 / 3

Raise both sides to the power of two

x = 16 / 9

I will assume you mean

√(9+x) - √x = 5/√(9+x)

Entering it into Wolfram the way you typed it ....
www.wolframalpha.com/input/?i=solve+%E2%88%9A9%2Bx+-+%E2%88%9Ax%3D5%2F%E2%88%9A9%2Bx

If √(9+x) - √x = 5/√(9+x) , then multiply both sides by √(9+x)
√(9+x)^2 - √x√(9+x) = 5
√(9+x)^2 - 5 = √x√(9+x)
9+x - 5 = √(x(9+x))
4+x = √(x(9+x))
square both sides
16 + 8x + x^2 = 9x + x^2
x = 16

Since we squared, all answers MUST be verified in the original equation
if x = 16
LS = √(9+16) - √16 = 5-4 = 1
RS = 5/√(9+16) = 5/√25 = 1

x = 16

To solve this equation, let's go step by step.

First, we can simplify the equation by rationalizing the denominators. The denominator on the right side of the equation is already rationalized, so we only need to deal with the denominator on the left side.

√9 + x can be written as (√9 + x) * (√9 + x). This simplifies to 9 + 2√9x + x^2. Now our equation becomes:

9 + 2√9x + x^2 - √x = 5 / (√9 + x)

Next, let's isolate the square roots. Move the √x term to the left side and the other terms to the right side:

2√9x + x^2 - √x - 5 / (√9 + x) = 9

Now, let's focus on simplifying the expression on the left side. To combine the terms, we can multiply (√9 + x) to both the numerator and denominator of the fraction:

[2√9x + x^2 - √x(√9 + x) - 5*(√9 + x)] / (√9 + x) = 9

Expanding the terms, we have:

[2√9x + x^2 - (√x * √9) - (√x * x) - (5 * √9) - (5 * x)] / (√9 + x) = 9

Simplifying further:

[2√9x + x^2 - 3√x - x√x - 5√9 - 5x] / (√9 + x) = 9

Now, let's combine the like terms:

[x^2 + 2√9x - x√x - 3√x - 5√9 - 5x] / (√9 + x) = 9

Next, let's simplify the radicals. √9 is equal to 3 and √x * √9 is equal to √9x:

[x^2 + 2√9x - x√x - 3√x - 5√9 - 5x] / (√9 + x) = 9

[x^2 + 6x - x√x - 3√x - 15 - 5x] / (√9 + x) = 9

Combine the like terms:

[x^2 + x - x√x - 3√x - 15] / (√9 + x) = 9

Now, let's multiply both sides of the equation by (√9 + x) to eliminate the fraction:

[x^2 + x - x√x - 3√x - 15] = 9 * (√9 + x)

Simplifying further:

x^2 + x - x√x - 3√x - 15 = 9√9 + 9x

Rearranging the equation:

x^2 + x - x√x - 3√x - 9x - 9√9 - 15 = 0

Now we have a quadratic equation in terms of x and √x. To solve this equation, we can use the quadratic formula or factorization methods.