Solve p+5/p-4=p/p+6

$$\frac { p + 5 } { p - 4 } = \frac { p } { p + 6 }$$

Solve for p

$$p=-2$$

Steps for Solving Linear Equation

Variable p cannot be equal to any of the values -6,4 since division by zero is not defined. Multiply both sides of the equation by \left(p-4\right)\left(p+6\right), the least common multiple of p-4,p+6.

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

Use the distributive property to multiply p+6 by p+5 and combine like terms.

$$p^{2}+11p+30=\left(p-4\right)p$$

Use the distributive property to multiply p-4 by p.

$$p^{2}+11p+30=p^{2}-4p$$

Subtract p^{2} from both sides.

$$p^{2}+11p+30-p^{2}=-4p$$

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

$$11p+30=-4p$$

Add 4p to both sides.

$$11p+30+4p=0$$

Combine 11p and 4p to get 15p.

$$15p+30=0$$

Subtract 30 from both sides. Anything subtracted from zero gives its negation.

$$15p=-30$$

Divide both sides by 15.

$$p=\frac{-30}{15}$$

Divide -30 by 15 to get -2.

$$p=-2$$