Solve 15/p+6p-5/p+2=6

$$\frac{ 15 }{ p } + \frac{ 6p-5 }{ p+2 } = 6$$

Solve for p

$$p=15$$

Steps for Solving Linear Equation

Variable p cannot be equal to any of the values -2,0 since division by zero is not defined. Multiply both sides of the equation by p\left(p+2\right), the least common multiple of p,p+2.

$$\left(p+2\right)\times 15+p\left(6p-5\right)=6p\left(p+2\right)$$

Use the distributive property to multiply p+2 by 15.

$$15p+30+p\left(6p-5\right)=6p\left(p+2\right)$$

Use the distributive property to multiply p by 6p-5.

$$15p+30+6p^{2}-5p=6p\left(p+2\right)$$

Combine 15p and -5p to get 10p.

$$10p+30+6p^{2}=6p\left(p+2\right)$$

Use the distributive property to multiply 6p by p+2.

$$10p+30+6p^{2}=6p^{2}+12p$$

Subtract 6p^{2} from both sides.

$$10p+30+6p^{2}-6p^{2}=12p$$

Combine 6p^{2} and -6p^{2} to get 0.

$$10p+30=12p$$

Subtract 12p from both sides.

$$10p+30-12p=0$$

Combine 10p and -12p to get -2p.

$$-2p+30=0$$

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

$$-2p=-30$$

Divide both sides by -2.

$$p=\frac{-30}{-2}$$

Divide -30 by -2 to get 15.

$$p=15$$