Solve 3x/x-7=sqrt{7}

$$\frac { 3 x } { x - 7 } = \sqrt { 7 }$$

Solve for x

$$x=\frac{-21\sqrt{7}-49}{2}\approx -52.280388766$$

Steps for Solving Linear Equation

Variable x cannot be equal to 7 since division by zero is not defined. Multiply both sides of the equation by x-7.

$$3x=\left(x-7\right)\sqrt{7}$$

Use the distributive property to multiply x-7 by \sqrt{7}.

$$3x=x\sqrt{7}-7\sqrt{7}$$

Subtract x\sqrt{7} from both sides.

$$3x-x\sqrt{7}=-7\sqrt{7}$$

Reorder the terms.

$$-\sqrt{7}x+3x=-7\sqrt{7}$$

Combine all terms containing x.

$$\left(-\sqrt{7}+3\right)x=-7\sqrt{7}$$

The equation is in standard form.

$$\left(3-\sqrt{7}\right)x=-7\sqrt{7}$$

Divide both sides by -\sqrt{7}+3.

$$\frac{\left(3-\sqrt{7}\right)x}{3-\sqrt{7}}=-\frac{7\sqrt{7}}{3-\sqrt{7}}$$

Dividing by -\sqrt{7}+3 undoes the multiplication by -\sqrt{7}+3.

$$x=-\frac{7\sqrt{7}}{3-\sqrt{7}}$$

Divide -7\sqrt{7} by -\sqrt{7}+3.

$$x=\frac{-21\sqrt{7}-49}{2}$$