Solve y=1+4/sqrt{-x}

$$y=1+ \frac{ 4 }{ \sqrt{ -x } }$$

Solve for y

$$y=1+\frac{4}{\sqrt{-x}}$$

$$x<0$$

Short Solution Steps

Factor \sqrt{-x}.

$$y=1+\frac{4}{\sqrt{-1}\sqrt{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\sqrt{-1}\sqrt{x}}{\sqrt{-1}\sqrt{x}}.

$$y=\frac{\sqrt{-1}\sqrt{x}}{\sqrt{-1}\sqrt{x}}+\frac{4}{\sqrt{-1}\sqrt{x}}$$

Since \frac{\sqrt{-1}\sqrt{x}}{\sqrt{-1}\sqrt{x}} and \frac{4}{\sqrt{-1}\sqrt{x}} have the same denominator, add them by adding their numerators.

$$y=\frac{\sqrt{-1}\sqrt{x}+4}{\sqrt{-1}\sqrt{x}}$$

Do the multiplications in \sqrt{-1}\sqrt{x}+4.

$$y=\frac{\text{Indeterminate}}{\sqrt{-1}\sqrt{x}}$$

Reorder the terms.

$$y=\text{Indeterminate}$$

Solve for x

$$x=-\frac{16}{\left(y-1\right)^{2}}$$

$$y>1$$