What is (x^2+4x+4)/(x^2-4) ?

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

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simplify (x^2+4x+4)/(x^2-4)

simplify

\frac{x ^{2} + 4 x + 4}{x ^{2} - 4}

\frac{x + 2}{x - 2}

Solution steps

\frac{x ^{2} + 4 x + 4}{x ^{2} - 4}

Factor

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

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

Factor

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

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

Apply exponent rule:

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

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

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

Cancel the common factor:

x + 2

= \frac{x + 2}{x - 2}

\frac{2 x + 14}{x ^{2} + 6 x - 7}

2 x - 3 x - x

10 \times 10

(m + n)^{2}

(x - 3) (x - 6)