Reducing of Rational Fractions

To reduce fraction means to divide the numerator and denominator by common multiplier.

Posibility of such reduction is conditional by basic property of fraction.

In order to reduce rational fraction, we should factoring the numerator and denominator.

If the numerator and denominator have common multipliers, then we can reduce the fraction.

If there is no the common multipliers, then we can′t reduce the fraction.

Example. Reduce the following fraction: `(x^2-3xy)/(9y^2-x^2)` .

We have `x^2-3xy=x(x-3y)`;

`9y^2-x^2=-(x^2-9y^2)=-(x+3y)(x-3y)`.

So, `(x^2-3xy)/(9y^2-x^2)=(x color(red)((x-3y)))/(-(x+3y) color(red)((x+3y)))=-x/(x+3y)` .

In fact, the reducing of fraction is performed for `x-3y!=0`.