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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

4 x^{3} y^{2} + 18 x y^{3} - 30 x^{2} y

(- x^{2} - 4 x - 5) + (- x^{2} + 8 x + 8)

(4 x^{2} - 8 x - 2) (x^{4} + 3 x^{2} + 4 x)

x^{3} + x^{3}

(x + 4) (x - 5)