What is 1/(x^2-4x+4)+2 ?

The solution to 1/(x^2-4x+4)+2 is (2x^2-8x+9)/(x^2-4x+4)

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simplify 1/(x^2-4x+4)+2

simplify

\frac{1}{x ^{2} - 4 x + 4} + 2

\frac{2 x ^{2} - 8 x + 9}{x ^{2} - 4 x + 4}

Solution steps

\frac{1}{x ^{2} - 4 x + 4} + 2

Apply the fraction rule:

a + \frac{b}{c} = \frac{a c + b}{c}

= \frac{2 ( x ^{2} - 4 x + 4 ) + 1}{x ^{2} - 4 x + 4}

Simplify

2 (x^{2} - 4 x + 4) + 1 : 2 x^{2} - 8 x + 9

= \frac{2 x ^{2} - 8 x + 9}{x ^{2} - 4 x + 4}

(1 + x) (2 - x) - (3 - x) (3 + x)

4 x^{3} + 7 x^{2} + 4 x + 7

9 x^{2} y^{7}

(- 3) - (- 1)

25 b^{2} - 144

What is 1/(x^2-4x+4)+2 ?
The solution to 1/(x^2-4x+4)+2 is (2x^2-8x+9)/(x^2-4x+4)