# How do you express (17x-50)/(x^(2)-6x+8) in partial fractions?

Jun 13, 2018

$\frac{17 x - 50}{{x}^{2} - 6 x + 8} = \frac{8}{x - 2} + \frac{9}{x - 4}$

#### Explanation:

Note that:

${x}^{2} - 6 x + 8 = \left(x - 2\right) \left(x - 4\right)$

So:

$\frac{17 x - 50}{{x}^{2} - 6 x + 8} = \frac{A}{x - 2} + \frac{B}{x - 4}$

Multiplying both sides by ${x}^{2} - 6 x + 8$ this becomes:

$17 x - 50 = A \left(x - 4\right) + B \left(x - 2\right)$

Putting $x = 2$, we find:

$- 16 = 34 - 50 = 17 \left(\textcolor{b l u e}{2}\right) - 50 = A \left(\left(\textcolor{b l u e}{2}\right) - 4\right) = - 2 A$

Hence $A = 8$

Putting $x = 4$, we find:

$18 = 17 \left(\textcolor{b l u e}{4}\right) - 50 = B \left(\left(\textcolor{b l u e}{4}\right) - 2\right) = 2 B$

Hence $B = 9$