Algebraic fractions.

 

Simplify \[ \frac{x^2 + 2}{x^2 - x} - \frac{3}{x - 1} \ \]

Put everything over a common denominator.

\[ = \frac {(x^2+2) - 3x} {x(x-1)} \ \] \[ = \frac {x^2 - 3x + 2} {x(x-1)} \ \]

Factorise the numerator.

\[ = \frac {(x-2)(x-1)} {x(x-1)} \ \]

Cancel common factors.

\[ = \frac {x-2} {x} \ \]

You will gain most benefit if you work through each problem first and then come back and check your work against the solution.

 

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Now You Try:

Simplify \[ \frac{x^2 + x}{x^2 - 4} - \frac{4}{x - 2} \ \]