Solve sqrt{7}+frac{sqrt{5}}{x}=1

$$\sqrt { 7 } + \frac { \sqrt { 5 } } { x } = 1$$

Solve for x

$$x = -\frac{\sqrt{5} {(\sqrt{7} + 1)}}{6} \approx -1.358691293$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\sqrt{7}+\sqrt{5}=x$$

Subtract x from both sides.

$$x\sqrt{7}+\sqrt{5}-x=0$$

Subtract \sqrt{5} from both sides. Anything subtracted from zero gives its negation.

$$x\sqrt{7}-x=-\sqrt{5}$$

Combine all terms containing x.

$$\left(\sqrt{7}-1\right)x=-\sqrt{5}$$

Divide both sides by \sqrt{7}-1.

$$\frac{\left(\sqrt{7}-1\right)x}{\sqrt{7}-1}=-\frac{\sqrt{5}}{\sqrt{7}-1}$$

Dividing by \sqrt{7}-1 undoes the multiplication by \sqrt{7}-1.

$$x=-\frac{\sqrt{5}}{\sqrt{7}-1}$$

Divide -\sqrt{5} by \sqrt{7}-1.

$$x=-\frac{\sqrt{5}\left(\sqrt{7}+1\right)}{6}$$