What is the answer to sqrt(x)+sqrt(a+x)=((3a))/((sqrt(a+x))) ?

The answer to sqrt(x)+sqrt(a+x)=((3a))/((sqrt(a+x))) is x=(4a)/5 {a>0}

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sqrt(x)+sqrt(a+x)=((3a))/((sqrt(a+x)))

x + a + x = \frac{( 3 a )}{( a + x )}

x = \frac{4 a}{5} {a > 0}

Solution steps

x + a + x = \frac{( 3 a )}{( a + x )}

Multiply both sides by

a + x

x a + x + a + x a + x = \frac{3 a}{a + x} a + x

Simplify

x a + x + (a + x)^{2} = 3 a

Expand

x a + x + (a + x)^{2} : x a + x + a + x

x a + x + a + x = 3 a

Remove square roots

a x + x^{2} = 4 a^{2} - 4 a x + x^{2}

Solve

a x + x^{2} = 4 a^{2} - 4 a x + x^{2} : x = \frac{4 a}{5}

x = \frac{4 a}{5}

Verify Solutions:

x = \frac{4 a}{5} {a > 0}

The solution is

x = \frac{4 a}{5} {a > 0}

v, 5 w = \frac{( ( v + 2 ) ^{\frac{1}{2}} )}{3}

x, z = x y + y \cdot x^{2} - a^{2} + b

x^{2} + (x - 1)^{2} = 1

(2 x + 5)^{\frac{1}{3}} = 5

(x^{0.16}) + 80 = 122

What is the answer to sqrt(x)+sqrt(a+x)=((3a))/((sqrt(a+x))) ?
The answer to sqrt(x)+sqrt(a+x)=((3a))/((sqrt(a+x))) is x=(4a)/5 {a>0}