Solve 6/p-5-8/p-4

$$\frac { 6 } { p - 5 } - \frac { 8 } { p - 4 }$$

Evaluate

$$\frac{2\left(8-p\right)}{\left(p-5\right)\left(p-4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p-5 and p-4 is \left(p-5\right)\left(p-4\right). Multiply \frac{6}{p-5} times \frac{p-4}{p-4}. Multiply \frac{8}{p-4} times \frac{p-5}{p-5}.

$$\frac{6\left(p-4\right)}{\left(p-5\right)\left(p-4\right)}-\frac{8\left(p-5\right)}{\left(p-5\right)\left(p-4\right)}$$

Since \frac{6\left(p-4\right)}{\left(p-5\right)\left(p-4\right)} and \frac{8\left(p-5\right)}{\left(p-5\right)\left(p-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\left(p-4\right)-8\left(p-5\right)}{\left(p-5\right)\left(p-4\right)}$$

Do the multiplications in 6\left(p-4\right)-8\left(p-5\right).

$$\frac{6p-24-8p+40}{\left(p-5\right)\left(p-4\right)}$$

Combine like terms in 6p-24-8p+40.

$$\frac{-2p+16}{\left(p-5\right)\left(p-4\right)}$$

Expand \left(p-5\right)\left(p-4\right).

$$\frac{-2p+16}{p^{2}-9p+20}$$

Factor

$$\frac{2\left(8-p\right)}{\left(p-5\right)\left(p-4\right)}$$