What is (4-x^2)/(x^2-5x+6) ?

The solution to (4-x^2)/(x^2-5x+6) is -(2+x)/(x-3)

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simplify (4-x^2)/(x^2-5x+6)

simplify

\frac{4 - x ^{2}}{x ^{2} - 5 x + 6}

- \frac{2 + x}{x - 3}

Solution steps

\frac{4 - x ^{2}}{x ^{2} - 5 x + 6}

Factor

4 - x^{2} : (2 + x) (2 - x)

= \frac{( 2 + x ) ( 2 - x )}{x ^{2} - 5 x + 6}

Factor

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

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

(2 + x) (2 - x) = - (2 + x) (x - 2)

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

Cancel the common factor:

x - 2

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2 + x}{x - 3}

2 - 2 x^{2}

\frac{\frac{2 x - 5}{4}}{\frac{x + 3}{4}}

\frac{x ^{2} - 64}{x ^{2} - 11 x + 24}

(- 2 - i)^{2}

\frac{80}{60}