Question

Сократить дробь ax-ay-x^2+xy/ax-a^2

Answer 1

$\frac{ax-ay-x^{2}+xy }{ax-a^{2} }=\frac{(ax-ay)-(x^{2}-xy) }{a(x-a)}=\frac{a(x-y)-x(x-y)}{a(x-a)}=\frac{(x-y)(a-x)}{a(x-a)}=-\frac{x-y}{a}=\frac{y-x}{a}$

Answer 2

To simplify the given fraction, we need to factorize the numerator and the denominator and then cancel out common factors. Let's start by factoring the numerator and the denominator:

Numerator: ax - ay - x^2 + xy

Factor out common terms: a(x - y) - x(x - y)

Numerator after factoring: (a - x)(x - y)

Denominator: ax - a^2

Factor out common term: a(x - a)

Now, the fraction becomes:

[(a - x)(x - y)] / [a(x - a)]

Since (a - x) and (x - y) appear in both the numerator and the denominator, we can cancel them out:

= (a - x) / a

The simplified fraction is (a - x) / a.