Solve frac{6-sqrt{2}}{5+x}-3=0

$$\frac { 6 - \sqrt { 2 } } { 5 + x } - 3 = 0$$

Solve for x

$$x=-\frac{\sqrt{2}}{3}-3\approx -3.471404521$$

Steps for Solving Linear Equation

Variable x cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by x+5.

$$6-\sqrt{2}+\left(x+5\right)\left(-3\right)=0$$

Use the distributive property to multiply x+5 by -3.

$$6-\sqrt{2}-3x-15=0$$

Subtract 15 from 6 to get -9.

$$-9-\sqrt{2}-3x=0$$

Add 9 to both sides. Anything plus zero gives itself.

$$-\sqrt{2}-3x=9$$

Add \sqrt{2} to both sides.

$$-3x=9+\sqrt{2}$$

The equation is in standard form.

$$-3x=\sqrt{2}+9$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{\sqrt{2}+9}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{\sqrt{2}+9}{-3}$$

Divide 9+\sqrt{2} by -3.

$$x=-\frac{\sqrt{2}}{3}-3$$