What is the answer to sqrt(1+x)+(ax)/(sqrt(1+x))=0 ?

The answer to sqrt(1+x)+(ax)/(sqrt(1+x))=0 is x=-1/(1+a) {a 0}

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sqrt(1+x)+(ax)/(sqrt(1+x))=0

1 + x + \frac{a x}{1 + x} = 0

x = - \frac{1}{1 + a} {a < - 1 or a > 0}

Solution steps

1 + x + \frac{a x}{1 + x} = 0

Multiply both sides by

1 + x

1 + x 1 + x + \frac{a x}{1 + x} 1 + x = 0 \cdot 1 + x

Simplify

(1 + x)^{2} + a x = 0

Expand

(1 + x)^{2} + a x : 1 + x + a x

1 + x + a x = 0

Solve

1 + x + a x = 0 : x = - \frac{1}{1 + a}

x = - \frac{1}{1 + a}

Verify Solutions:

x = - \frac{1}{1 + a} {a < - 1 or a > 0}

The solution is

x = - \frac{1}{1 + a} {a < - 1 or a > 0}

2 x - 3 x - 2 = 0

\frac{1}{2} x - x = 0

x, x + 15 + x = 15

40 - x^{2} = 3 x

x + 5 - 1 = 4 x - 12

What is the answer to sqrt(1+x)+(ax)/(sqrt(1+x))=0 ?
The answer to sqrt(1+x)+(ax)/(sqrt(1+x))=0 is x=-1/(1+a) {a<-1\lor a>0}