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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x - 2 + (x - 1) x : x^{2} - 2

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

- 4 + (- 10)

13 (9 - 6 m) + 14 (12 m - 8)

\frac{1}{3} \times \frac{3}{5}

[0.2 π]

2 0^{2}

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