√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
√9+x - √x=5/√9+x
2 answers
I will assume you mean
√(9+x) - √x = 5/√(9+x)
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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
√(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