Solve 3/p^2+5p+6+2/p^2+8p+12=4/p^2+9p+18

$$\frac { 3 } { p ^ { 2 } + 5 p + 6 } + \frac { 2 } { p ^ { 2 } + 8 p + 12 } = \frac { 4 } { p ^ { 2 } + 9 p + 18 }$$

Solve for p

$$p=-16$$

Steps for Solving Linear Equation

Variable p cannot be equal to any of the values -6,-3,-2 since division by zero is not defined. Multiply both sides of the equation by \left(p+2\right)\left(p+3\right)\left(p+6\right), the least common multiple of p^{2}+5p+6,p^{2}+8p+12,p^{2}+9p+18.

$$\left(p+6\right)\times 3+\left(p+3\right)\times 2=\left(p+2\right)\times 4$$

Use the distributive property to multiply p+6 by 3.

$$3p+18+\left(p+3\right)\times 2=\left(p+2\right)\times 4$$

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

$$3p+18+2p+6=\left(p+2\right)\times 4$$

Combine 3p and 2p to get 5p.

$$5p+18+6=\left(p+2\right)\times 4$$

Add 18 and 6 to get 24.

$$5p+24=\left(p+2\right)\times 4$$

Use the distributive property to multiply p+2 by 4.

$$5p+24=4p+8$$

Subtract 4p from both sides.

$$5p+24-4p=8$$

Combine 5p and -4p to get p.

$$p+24=8$$

Subtract 24 from both sides.

$$p=8-24$$

Subtract 24 from 8 to get -16.

$$p=-16$$