Question

Сократить (x^2-yz+xz-y^2)/(x^2+yz-xz-y^2)=

Answer 1

$\frac{ {x}^{2} - yz + xz - {y}^{2} } { {x}^{2} + yz - xz - {y}^{2} } = \\ = \frac{(x ^{2} - y^{2} ) + z(x - y)}{(x ^{2} - y^{2} ) - z(x - y)} = \\ \frac{(x - y)(x + y) + z(x - y) }{(x - y)(x + y) - z(x - y)} = \\ = \frac{(x - y)(x + y + z)}{(x - y)(x + y - z)} = \\ = \frac{x + y + z}{x + y - z}$

Answer 2

To simplify the expression $\frac{{x^2-yz+xz-y^2}}{{x^2+yz-xz-y^2}}$, we can factor the numerator and the denominator and then simplify by canceling common terms. Let's go step by step:

1. Factor the numerator and the denominator: $\frac{{x^2-yz+xz-y^2}}{{x^2+yz-xz-y^2}} = \frac{{(x^2 - y^2) + (xz - yz)}}{{(x^2 - y^2) + (xz - yz)}}$

2. Observe that $(x^2 - y^2) + (xz - yz)$ appears in both the numerator and the denominator.

3. Cancel out the common terms: $\frac{{(x^2 - y^2) + (xz - yz)}}{{(x^2 - y^2) + (xz - yz)}} = 1$

Therefore, the simplified expression is $1$.