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

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

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

simplify

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

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

Solution steps

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

Factor

x^{2} - 6 x + 9 : (x - 3)^{2}

= \frac{( x - 3 ) ^{2}}{x ^{2} - 9}

Factor

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

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Cancel the common factor:

x - 3

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

(2 x - 1) (x + 3)

- 3 a (a^{2} - 10 a + 25)

5 x^{0}

\frac{18}{8}

x^{2} - \frac{1}{4}