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

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

Solve for p

$$p=-13$$

Steps for Solving Linear Equation

Variable p cannot be equal to any of the values 2,5 since division by zero is not defined. Multiply both sides of the equation by \left(p-5\right)\left(p-2\right), the least common multiple of p-5,p-2.

$$\left(p-2\right)\left(p+1\right)=\left(p-5\right)\left(p+3\right)$$

Use the distributive property to multiply p-2 by p+1 and combine like terms.

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

Use the distributive property to multiply p-5 by p+3 and combine like terms.

$$p^{2}-p-2=p^{2}-2p-15$$

Subtract p^{2} from both sides.

$$p^{2}-p-2-p^{2}=-2p-15$$

Combine p^{2} and -p^{2} to get 0.

$$-p-2=-2p-15$$

Add 2p to both sides.

$$-p-2+2p=-15$$

Combine -p and 2p to get p.

$$p-2=-15$$

Add 2 to both sides.

$$p=-15+2$$

Add -15 and 2 to get -13.

$$p=-13$$