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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x - 2

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

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

b^{2} - 4 b + 3

\frac{3}{4} - \frac{1}{2}

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

3 \times \frac{2}{4}