Solve p+2=p+2/p-3

$$p + 2 = \frac { p + 2 } { p - 3 }$$

Solve for p

$$p=-2$$

$$p=4$$

Steps Using the Quadratic Formula

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

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

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

$$p^{2}-3p+\left(p-3\right)\times 2=p+2$$

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

$$p^{2}-3p+2p-6=p+2$$

Combine -3p and 2p to get -p.

$$p^{2}-p-6=p+2$$

Subtract p from both sides.

$$p^{2}-p-6-p=2$$

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

$$p^{2}-2p-6=2$$

Subtract 2 from both sides.

$$p^{2}-2p-6-2=0$$

Subtract 2 from -6 to get -8.

$$p^{2}-2p-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -2 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-8\right)}}{2}$$

Square -2.

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

Multiply -4 times -8.

$$p=\frac{-\left(-2\right)±\sqrt{4+32}}{2}$$

Add 4 to 32.

$$p=\frac{-\left(-2\right)±\sqrt{36}}{2}$$

Take the square root of 36.

$$p=\frac{-\left(-2\right)±6}{2}$$

The opposite of -2 is 2.

$$p=\frac{2±6}{2}$$

Now solve the equation p=\frac{2±6}{2} when ± is plus. Add 2 to 6.

$$p=\frac{8}{2}$$

Divide 8 by 2.

$$p=4$$

Now solve the equation p=\frac{2±6}{2} when ± is minus. Subtract 6 from 2.

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

Divide -4 by 2.

$$p=-2$$

The equation is now solved.

$$p=4 p=-2$$

Steps for Completing the Square

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

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

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

$$p^{2}-3p+\left(p-3\right)\times 2=p+2$$

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

$$p^{2}-3p+2p-6=p+2$$

Combine -3p and 2p to get -p.

$$p^{2}-p-6=p+2$$

Subtract p from both sides.

$$p^{2}-p-6-p=2$$

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

$$p^{2}-2p-6=2$$

Add 6 to both sides.

$$p^{2}-2p=2+6$$

Add 2 and 6 to get 8.

$$p^{2}-2p=8$$

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$p^{2}-2p+1=8+1$$

Add 8 to 1.

$$p^{2}-2p+1=9$$

Factor p^{2}-2p+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(p-1\right)^{2}=9$$

Take the square root of both sides of the equation.

$$\sqrt{\left(p-1\right)^{2}}=\sqrt{9}$$

Simplify.

$$p-1=3 p-1=-3$$

Add 1 to both sides of the equation.

$$p=4 p=-2$$