Solve 2y/1-2-4/y-2=4

$$\frac { 2 y } { 1 - 2 } - \frac { 4 } { y - 2 } = 4$$

Solve for y

$$y=\sqrt{2}\approx 1.414213562$$

$$y=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Variable y cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by y-2.

$$\left(-y+2\right)\times 2y-4=4\left(y-2\right)$$

Use the distributive property to multiply -y+2 by 2.

$$\left(-2y+4\right)y-4=4\left(y-2\right)$$

Use the distributive property to multiply -2y+4 by y.

$$-2y^{2}+4y-4=4\left(y-2\right)$$

Use the distributive property to multiply 4 by y-2.

$$-2y^{2}+4y-4=4y-8$$

Subtract 4y from both sides.

$$-2y^{2}+4y-4-4y=-8$$

Combine 4y and -4y to get 0.

$$-2y^{2}-4=-8$$

Add 4 to both sides.

$$-2y^{2}=-8+4$$

Add -8 and 4 to get -4.

$$-2y^{2}=-4$$

Divide both sides by -2.

$$y^{2}=\frac{-4}{-2}$$

Divide -4 by -2 to get 2.

$$y^{2}=2$$

Take the square root of both sides of the equation.

$$y=\sqrt{2} y=-\sqrt{2}$$

Steps Using the Quadratic Formula

Variable y cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by y-2.

$$\left(-y+2\right)\times 2y-4=4\left(y-2\right)$$

Use the distributive property to multiply -y+2 by 2.

$$\left(-2y+4\right)y-4=4\left(y-2\right)$$

Use the distributive property to multiply -2y+4 by y.

$$-2y^{2}+4y-4=4\left(y-2\right)$$

Use the distributive property to multiply 4 by y-2.

$$-2y^{2}+4y-4=4y-8$$

Subtract 4y from both sides.

$$-2y^{2}+4y-4-4y=-8$$

Combine 4y and -4y to get 0.

$$-2y^{2}-4=-8$$

Add 8 to both sides.

$$-2y^{2}-4+8=0$$

Add -4 and 8 to get 4.

$$-2y^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 4}}{2\left(-2\right)}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-2\right)\times 4}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$y=\frac{0±\sqrt{8\times 4}}{2\left(-2\right)}$$

Multiply 8 times 4.

$$y=\frac{0±\sqrt{32}}{2\left(-2\right)}$$

Take the square root of 32.

$$y=\frac{0±4\sqrt{2}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$y=\frac{0±4\sqrt{2}}{-4}$$

Now solve the equation y=\frac{0±4\sqrt{2}}{-4} when ± is plus.

$$y=-\sqrt{2}$$

Now solve the equation y=\frac{0±4\sqrt{2}}{-4} when ± is minus.

$$y=\sqrt{2}$$

The equation is now solved.

$$y=-\sqrt{2} y=\sqrt{2}$$