What is (x+3)/(x^4-81) ?

The solution to (x+3)/(x^4-81) is 1/((x^2+9)(x-3))

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simplify (x+3)/(x^4-81)

simplify

\frac{x + 3}{x ^{4} - 81}

\frac{1}{( x ^{2} + 9 ) ( x - 3 )}

Solution steps

\frac{x + 3}{x ^{4} - 81}

Apply exponent rules

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

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

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

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

Factor

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

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

Cancel the common factor:

x + 3

= \frac{1}{( x ^{2} + 9 ) ( x - 3 )}

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

\frac{72}{8 + 98}

327 - 3

20 c^{2} - 45 d^{2}