What is h/(h^2-5h+6)+3/(3-h) ?

The solution to h/(h^2-5h+6)+3/(3-h) is -2/(h-2)

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simplify h/(h^2-5h+6)+3/(3-h)

simplify

\frac{h}{h ^{2} - 5 h + 6} + \frac{3}{3 - h}

- \frac{2}{h - 2}

Solution steps

\frac{h}{h ^{2} - 5 h + 6} + \frac{3}{3 - h}

Least Common Multiplier of

h^{2} - 5 h + 6, 3 - h : (h - 2) (h - 3) (- h + 3)

Adjust Fractions based on the LCM

= \frac{h ( - h + 3 )}{( h - 2 ) ( h - 3 ) ( - h + 3 )} + \frac{- 3 ( h - 2 ) ( - h + 3 )}{( h - 2 ) ( h - 3 ) ( - h + 3 )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{h ( - h + 3 ) - 3 ( h - 2 ) ( - h + 3 )}{( h - 2 ) ( h - 3 ) ( - h + 3 )}

Simplify

h (- h + 3) - 3 (h - 2) (- h + 3) : 2 h^{2} - 12 h + 18

= \frac{2 h ^{2} - 12 h + 18}{( h - 2 ) ( h - 3 ) ( - h + 3 )}

Cancel

\frac{2 h ^{2} - 12 h + 18}{( h - 2 ) ( h - 3 ) ( - h + 3 )} : - \frac{2}{h - 2}

= - \frac{2}{h - 2}

\frac{1 - 6 i}{8 + 7 i}

(x - 8) (x - 4)

- 4 y - 4 + (- 3)

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