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}

(5 - 2 x^{4}) (5 + 2 x^{4})

- y^{2} + 3 y^{2} + 2 y^{2}

4 x^{0}

2 ln (e^{6}) - ln (e^{5})

- 9 \div 3