What is (x^2+8x+16)/(x^2-16) ?

The solution to (x^2+8x+16)/(x^2-16) is (x+4)/(x-4)

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simplify (x^2+8x+16)/(x^2-16)

simplify

\frac{x ^{2} + 8 x + 16}{x ^{2} - 16}

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

Solution steps

\frac{x ^{2} + 8 x + 16}{x ^{2} - 16}

Factor

x^{2} + 8 x + 16 : (x + 4)^{2}

= \frac{( x + 4 ) ^{2}}{x ^{2} - 16}

Factor

x^{2} - 16 : (x + 4) (x - 4)

= \frac{( x + 4 ) ^{2}}{( x + 4 ) ( x - 4 )}

Apply exponent rule:

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

(x + 4)^{2} = (x + 4) (x + 4)

= \frac{( x + 4 ) ( x + 4 )}{( x + 4 ) ( x - 4 )}

Cancel the common factor:

x + 4

= \frac{x + 4}{x - 4}

\frac{60}{24}

\frac{2}{54}

a^{2} b^{3} - 3 a^{2} b^{3} + 8 a^{2} b^{3} - 5 a^{2} b^{3} + 4 a^{2} b^{3}

(2 x - 4) (3 x + 5)

(x - 5)^{2}

What is (x^2+8x+16)/(x^2-16) ?
The solution to (x^2+8x+16)/(x^2-16) is (x+4)/(x-4)