Solve 6x-1/x-3=4sqrt{2}

$$\frac { 6 x - 1 } { x - 3 } = 4 \sqrt { 2 }$$

Solve for x

$$x=-17\sqrt{2}-\frac{45}{2}\approx -46.54163056$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$6x-1=4\sqrt{2}\left(x-3\right)$$

Use the distributive property to multiply 4\sqrt{2} by x-3.

$$6x-1=4\sqrt{2}x-12\sqrt{2}$$

Subtract 4\sqrt{2}x from both sides.

$$6x-1-4\sqrt{2}x=-12\sqrt{2}$$

Add 1 to both sides.

$$6x-4\sqrt{2}x=-12\sqrt{2}+1$$

Combine all terms containing x.

$$\left(6-4\sqrt{2}\right)x=-12\sqrt{2}+1$$

The equation is in standard form.

$$\left(6-4\sqrt{2}\right)x=1-12\sqrt{2}$$

Divide both sides by 6-4\sqrt{2}.

$$\frac{\left(6-4\sqrt{2}\right)x}{6-4\sqrt{2}}=\frac{1-12\sqrt{2}}{6-4\sqrt{2}}$$

Dividing by 6-4\sqrt{2} undoes the multiplication by 6-4\sqrt{2}.

$$x=\frac{1-12\sqrt{2}}{6-4\sqrt{2}}$$

Divide -12\sqrt{2}+1 by 6-4\sqrt{2}.

$$x=-17\sqrt{2}-\frac{45}{2}$$