Solve 5/p^2-p-20=5/p+4+3/p^2-p-20

$$\frac { 5 } { p ^ { 2 } - p - 20 } = \frac { 5 } { p + 4 } + \frac { 3 } { p ^ { 2 } - p - 20 }$$

Solve for p

$$p = \frac{27}{5} = 5\frac{2}{5} = 5.4$$

Steps for Solving Linear Equation

Variable p cannot be equal to any of the values -4,5 since division by zero is not defined. Multiply both sides of the equation by \left(p-5\right)\left(p+4\right), the least common multiple of p^{2}-p-20,p+4.

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

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

$$5=5p-25+3$$

Add -25 and 3 to get -22.

$$5=5p-22$$

Swap sides so that all variable terms are on the left hand side.

$$5p-22=5$$

Add 22 to both sides.

$$5p=5+22$$

Add 5 and 22 to get 27.

$$5p=27$$

Divide both sides by 5.

$$p=\frac{27}{5}$$