What is (x^2+16x+64)/(x^2-64) ?

The solution to (x^2+16x+64)/(x^2-64) is (x+8)/(x-8)

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simplify (x^2+16x+64)/(x^2-64)

simplify

\frac{x ^{2} + 16 x + 64}{x ^{2} - 64}

\frac{x + 8}{x - 8}

Solution steps

\frac{x ^{2} + 16 x + 64}{x ^{2} - 64}

Factor

x^{2} + 16 x + 64 : (x + 8)^{2}

= \frac{( x + 8 ) ^{2}}{x ^{2} - 64}

Factor

x^{2} - 64 : (x + 8) (x - 8)

= \frac{( x + 8 ) ^{2}}{( x + 8 ) ( x - 8 )}

Apply exponent rule:

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

(x + 8)^{2} = (x + 8) (x + 8)

= \frac{( x + 8 ) ( x + 8 )}{( x + 8 ) ( x - 8 )}

Cancel the common factor:

x + 8

= \frac{x + 8}{x - 8}

(5 y)^{2} + 13 (5 y) + 42

6 (9 a - 3 b) - 8 (2 a + 4 b)

5 x^{2} + 2 x^{2}

\frac{1}{2} - \frac{5}{16}

\frac{1}{24}

What is (x^2+16x+64)/(x^2-64) ?
The solution to (x^2+16x+64)/(x^2-64) is (x+8)/(x-8)