Solve p-2/2p^2+1/6p=p-5/3p^2

$$\frac { p - 2 } { 2 p ^ { 2 } } + \frac { 1 } { 6 p } = \frac { p - 5 } { 3 p ^ { 2 } }$$

Solve for p

$$p=-2$$

Steps for Solving Linear Equation

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6p^{2}, the least common multiple of 2p^{2},6p,3p^{2}.

$$3\left(p-2\right)+p=2\left(p-5\right)$$

Use the distributive property to multiply 3 by p-2.

$$3p-6+p=2\left(p-5\right)$$

Combine 3p and p to get 4p.

$$4p-6=2\left(p-5\right)$$

Use the distributive property to multiply 2 by p-5.

$$4p-6=2p-10$$

Subtract 2p from both sides.

$$4p-6-2p=-10$$

Combine 4p and -2p to get 2p.

$$2p-6=-10$$

Add 6 to both sides.

$$2p=-10+6$$

Add -10 and 6 to get -4.

$$2p=-4$$

Divide both sides by 2.

$$p=\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$p=-2$$