Solve -9p/p^2-4-8/p-2=1/p+2

$$\frac { - 9 p } { p ^ { 2 } - 4 } - \frac { 8 } { p - 2 } = \frac { 1 } { p + 2 }$$

Solve for p

$$p=-\frac{7}{9}\approx -0.777777778$$

Steps for Solving Linear Equation

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

$$-9p-\left(p+2\right)\times 8=p-2$$

Use the distributive property to multiply p+2 by 8.

$$-9p-\left(8p+16\right)=p-2$$

To find the opposite of 8p+16, find the opposite of each term.

$$-9p-8p-16=p-2$$

Combine -9p and -8p to get -17p.

$$-17p-16=p-2$$

Subtract p from both sides.

$$-17p-16-p=-2$$

Combine -17p and -p to get -18p.

$$-18p-16=-2$$

Add 16 to both sides.

$$-18p=-2+16$$

Add -2 and 16 to get 14.

$$-18p=14$$

Divide both sides by -18.

$$p=\frac{14}{-18}$$

Reduce the fraction \frac{14}{-18} to lowest terms by extracting and canceling out 2.

$$p=-\frac{7}{9}$$