What is (4-x^2)/(x^2-3x+2) ?

The solution to (4-x^2)/(x^2-3x+2) is -(2+x)/(x-1)

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simplify (4-x^2)/(x^2-3x+2)

simplify

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

- \frac{2 + x}{x - 1}

Solution steps

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

Factor

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

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

Factor

x^{2} - 3 x + 2 : (x - 1) (x - 2)

= \frac{( 2 + x ) ( 2 - x )}{( x - 1 ) ( x - 2 )}

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

= \frac{- ( 2 + x ) ( x - 2 )}{( x - 1 ) ( x - 2 )}

Cancel the common factor:

x - 2

= \frac{- ( 2 + x )}{x - 1}

Apply the fraction rule:

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

= - \frac{2 + x}{x - 1}

\frac{x ^{2} - 16}{x ^{2} + 6 x + 8}

(x + 1) 3

\frac{1}{x} - \frac{1}{3}

6724

\frac{0. 3 ^{5} \cdot 0. 3 ^{7}}{0. 3 ^{9}}