Solve frac{6+18P_{2}}{3P_{2}}+frac{4+8P_{2}}{4P_{2}}=17

$$\frac { 6 + 18 P _ { 2 } } { 3 P _ { 2 } } + \frac { 4 + 8 P _ { 2 } } { 4 P _ { 2 } } = 17$$

Solve for P_2

$$P_{2}=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

Variable P_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12P_{2}, the least common multiple of 3P_{2},4P_{2}.

$$4\left(6+18P_{2}\right)+3\left(4+8P_{2}\right)=204P_{2}$$

Use the distributive property to multiply 4 by 6+18P_{2}.

$$24+72P_{2}+3\left(4+8P_{2}\right)=204P_{2}$$

Use the distributive property to multiply 3 by 4+8P_{2}.

$$24+72P_{2}+12+24P_{2}=204P_{2}$$

Add 24 and 12 to get 36.

$$36+72P_{2}+24P_{2}=204P_{2}$$

Combine 72P_{2} and 24P_{2} to get 96P_{2}.

$$36+96P_{2}=204P_{2}$$

Subtract 204P_{2} from both sides.

$$36+96P_{2}-204P_{2}=0$$

Combine 96P_{2} and -204P_{2} to get -108P_{2}.

$$36-108P_{2}=0$$

Subtract 36 from both sides. Anything subtracted from zero gives its negation.

$$-108P_{2}=-36$$

Divide both sides by -108.

$$P_{2}=\frac{-36}{-108}$$

Reduce the fraction \frac{-36}{-108} to lowest terms by extracting and canceling out -36.

$$P_{2}=\frac{1}{3}$$