What is (\frac{x-2)/(x-1)}{(x^2-4)/(x^2+x-2)} ?

The solution to (\frac{x-2)/(x-1)}{(x^2-4)/(x^2+x-2)} is 1

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

simplify

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

1

Solution steps

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

Cancel

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

= \frac{\frac{x - 2}{x - 1}}{\frac{x - 2}{x - 1}}

Apply the fraction rule:

\frac{a}{a} = 1

= 1

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

\frac{3}{8} \cdot \frac{1}{2}

(13 + - 180) (6 + - 180)

(3 cos (t))^{2}

\frac{64}{5}

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