Solve P+4/P-2=1+Q/p-2

$$\frac { P + 4 } { P - 2 } = 1 + \frac { Q } { p - 2 }$$

Solve for P

$$P=\frac{2\left(3p+Q-6\right)}{Q}$$

$$p\neq 2\text{ and }Q\neq 0$$

Steps for Solving Linear Equation

Variable P cannot be equal to 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,p-2.

$$\left(p-2\right)\left(P+4\right)=\left(P-2\right)\left(p-2\right)+\left(P-2\right)Q$$

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

$$pP+4p-2P-8=\left(P-2\right)\left(p-2\right)+\left(P-2\right)Q$$

Use the distributive property to multiply P-2 by p-2.

$$pP+4p-2P-8=Pp-2P-2p+4+\left(P-2\right)Q$$

Use the distributive property to multiply P-2 by Q.

$$pP+4p-2P-8=Pp-2P-2p+4+PQ-2Q$$

Subtract Pp from both sides.

$$pP+4p-2P-8-Pp=-2P-2p+4+PQ-2Q$$

Combine pP and -Pp to get 0.

$$4p-2P-8=-2P-2p+4+PQ-2Q$$

Add 2P to both sides.

$$4p-2P-8+2P=-2p+4+PQ-2Q$$

Combine -2P and 2P to get 0.

$$4p-8=-2p+4+PQ-2Q$$

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

$$-2p+4+PQ-2Q=4p-8$$

Add 2p to both sides.

$$4+PQ-2Q=4p-8+2p$$

Combine 4p and 2p to get 6p.

$$4+PQ-2Q=6p-8$$

Subtract 4 from both sides.

$$PQ-2Q=6p-8-4$$

Subtract 4 from -8 to get -12.

$$PQ-2Q=6p-12$$

Add 2Q to both sides.

$$PQ=6p-12+2Q$$

The equation is in standard form.

$$QP=6p+2Q-12$$

Divide both sides by Q.

$$\frac{QP}{Q}=\frac{6p+2Q-12}{Q}$$

Dividing by Q undoes the multiplication by Q.

$$P=\frac{6p+2Q-12}{Q}$$

Divide -12+6p+2Q by Q.

$$P=\frac{2\left(3p+Q-6\right)}{Q}$$

Variable P cannot be equal to 2.

$$P=\frac{2\left(3p+Q-6\right)}{Q}\text{, }P\neq 2$$

Solve for Q

$$Q=-\frac{6\left(p-2\right)}{2-P}$$

$$P\neq 2\text{ and }p\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(P-2\right)\left(p-2\right), the least common multiple of P-2,p-2.

$$\left(p-2\right)\left(P+4\right)=\left(P-2\right)\left(p-2\right)+\left(P-2\right)Q$$

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

$$pP+4p-2P-8=\left(P-2\right)\left(p-2\right)+\left(P-2\right)Q$$

Use the distributive property to multiply P-2 by p-2.

$$pP+4p-2P-8=Pp-2P-2p+4+\left(P-2\right)Q$$

Use the distributive property to multiply P-2 by Q.

$$pP+4p-2P-8=Pp-2P-2p+4+PQ-2Q$$

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

$$Pp-2P-2p+4+PQ-2Q=pP+4p-2P-8$$

Subtract Pp from both sides.

$$-2P-2p+4+PQ-2Q=pP+4p-2P-8-Pp$$

Combine pP and -Pp to get 0.

$$-2P-2p+4+PQ-2Q=4p-2P-8$$

Add 2P to both sides.

$$-2p+4+PQ-2Q=4p-2P-8+2P$$

Combine -2P and 2P to get 0.

$$-2p+4+PQ-2Q=4p-8$$

Add 2p to both sides.

$$4+PQ-2Q=4p-8+2p$$

Combine 4p and 2p to get 6p.

$$4+PQ-2Q=6p-8$$

Subtract 4 from both sides.

$$PQ-2Q=6p-8-4$$

Subtract 4 from -8 to get -12.

$$PQ-2Q=6p-12$$

Combine all terms containing Q.

$$\left(P-2\right)Q=6p-12$$

Divide both sides by P-2.

$$\frac{\left(P-2\right)Q}{P-2}=\frac{6p-12}{P-2}$$

Dividing by P-2 undoes the multiplication by P-2.

$$Q=\frac{6p-12}{P-2}$$

Divide -12+6p by P-2.

$$Q=\frac{6\left(p-2\right)}{P-2}$$