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

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

Popular >

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

(2 + x) (2 - x) = - (2 + x) (x - 2)

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

Apply exponent rule:

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

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

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

Cancel the common factor:

x - 2

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

(- 10 x^{2} + 4 x) - (- 4 x^{2} + 6 x + 8)

16 (x + y)^{2} - 25 (x - 2 y)^{2}

\frac{4 a ^{16} + 2 b - 8}{2 ab}

\frac{8 x + 4}{2 x ^{2} - 5 x - 3}

\frac{6}{3 - 1}