What is (x^2+18x+81)/(x^2-81) ?

The solution to (x^2+18x+81)/(x^2-81) is (x+9)/(x-9)

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simplify (x^2+18x+81)/(x^2-81)

simplify

\frac{x ^{2} + 18 x + 81}{x ^{2} - 81}

\frac{x + 9}{x - 9}

Solution steps

\frac{x ^{2} + 18 x + 81}{x ^{2} - 81}

Factor

x^{2} + 18 x + 81 : (x + 9)^{2}

= \frac{( x + 9 ) ^{2}}{x ^{2} - 81}

Factor

x^{2} - 81 : (x + 9) (x - 9)

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

Apply exponent rule:

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

(x + 9)^{2} = (x + 9) (x + 9)

= \frac{( x + 9 ) ( x + 9 )}{( x + 9 ) ( x - 9 )}

Cancel the common factor:

x + 9

= \frac{x + 9}{x - 9}

54 x^{2} - 6 y^{2}

10 (- 1)

x^{2} - 2 x - 168

- 4 - 4

52 - 2

What is (x^2+18x+81)/(x^2-81) ?
The solution to (x^2+18x+81)/(x^2-81) is (x+9)/(x-9)