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}

5 + 7 (8 r - 2)

6 \times 6

\frac{4}{5} - \frac{3}{5}

(sin (x) cos (x))^{2}

0 - x