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

The solution to ((x+2)^2-8x)/((x-2)^2) is 1

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

simplify

\frac{( x + 2 ) ^{2} - 8 x}{( x - 2 ) ^{2}}

1

Solution steps

\frac{( x + 2 ) ^{2} - 8 x}{( x - 2 ) ^{2}}

Expand

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

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

Factor

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

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

Apply the fraction rule:

\frac{a}{a} = 1

= 1

(3 x + 2) (- 3 x^{2} - 7 x + 3)

\frac{5 8}{40} + 45

4 \frac{4}{5}

(2 - x)^{5}