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

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

Solve for p

$$p = \frac{22}{3} = 7\frac{1}{3} \approx 7.333333333$$

Steps for Solving Linear Equation

Variable p cannot be equal to any of the values 8,9 since division by zero is not defined. Multiply both sides of the equation by \left(p-9\right)\left(p-8\right), the least common multiple of p-8,p-9.

$$\left(p-9\right)\left(p-4\right)=\left(p-8\right)\left(p+1\right)$$

Use the distributive property to multiply p-9 by p-4 and combine like terms.

$$p^{2}-13p+36=\left(p-8\right)\left(p+1\right)$$

Use the distributive property to multiply p-8 by p+1 and combine like terms.

$$p^{2}-13p+36=p^{2}-7p-8$$

Subtract p^{2} from both sides.

$$p^{2}-13p+36-p^{2}=-7p-8$$

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

$$-13p+36=-7p-8$$

Add 7p to both sides.

$$-13p+36+7p=-8$$

Combine -13p and 7p to get -6p.

$$-6p+36=-8$$

Subtract 36 from both sides.

$$-6p=-8-36$$

Subtract 36 from -8 to get -44.

$$-6p=-44$$

Divide both sides by -6.

$$p=\frac{-44}{-6}$$

Reduce the fraction \frac{-44}{-6} to lowest terms by extracting and canceling out -2.

$$p=\frac{22}{3}$$