What is (x^2-9)/(x^2-5x+6) ?

The solution to (x^2-9)/(x^2-5x+6) is (x+3)/(x-2)

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simplify (x^2-9)/(x^2-5x+6)

simplify

\frac{x ^{2} - 9}{x ^{2} - 5 x + 6}

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

Solution steps

\frac{x ^{2} - 9}{x ^{2} - 5 x + 6}

Factor

x^{2} - 9 : (x + 3) (x - 3)

= \frac{( x + 3 ) ( x - 3 )}{x ^{2} - 5 x + 6}

Factor

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

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

Cancel the common factor:

x - 3

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

2 \cdot 3^{2} \cdot 5^{5}

\frac{1 0 ^{8} ( 1 0 ^{- 5} )}{1 0 ^{- 6}}

- 8108 + 12

\frac{1}{5} \times 2

(- 26)^{2}