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

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

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

simplify

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

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

Solution steps

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

Factor

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

= \frac{( x + 3 ) ( x - 3 )}{x ^{2} + 6 x + 9}

Factor

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

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

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}

- \frac{18}{2}

(5 - 1)!

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

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

- \frac{1}{2} \cdot 12 x