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

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

Solve for y

$$y=1$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by \left(y-2\right)\left(y+2\right), the least common multiple of y-2,y^{2}-4.

$$y+2=2y+1$$

Subtract 2y from both sides.

$$y+2-2y=1$$

Combine y and -2y to get -y.

$$-y+2=1$$

Subtract 2 from both sides.

$$-y=1-2$$

Subtract 2 from 1 to get -1.

$$-y=-1$$

Multiply both sides by -1.

$$y=1$$