Question

(x+y+x^2-y^2):(x-y+x^2-2xy+y^2)

Answer 1

Числит x+y+x²-y² знаменат x-y+x²-2xy+y²= разницу квадратов
                                          разложим, а квадрат разницы - свернём
числит х+у+(х-у)(х+у) знаменат х-у+(х-у)²= вынесем общее, тем самым
                                          разложив всё на множители
числит (х+у)(х-у+1) знаменат (х-у)(х-у+1)= сократим на длинную 
                                         скобочку
числит (х+у) знаменат (х-у).

Answer 2

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 3

To simplify the expression $\frac{x+y+x^2-y^2}{x-y+x^2-2xy+y^2}$, you can start by factoring the numerator and the denominator and then canceling common factors:

Numerator: $x+y+x^2-y^2$

1. Rearrange the terms: $x^2 - y^2 + x + y$
2. Factor using the difference of squares: $(x+y)(x-y) + x + y$

Denominator: $x-y+x^2-2xy+y^2$

1. Rearrange the terms: $x^2 - 2xy + y^2 - (x - y)$
2. Factor using the difference of squares: $(x-y)^2 - (x-y)$

Now, you can rewrite the expression with these factored forms:

$\frac{(x+y)(x-y) + x + y}{(x-y)^2 - (x-y)}$

Next, notice that both the numerator and the denominator have a common factor of $(x+y)$, so you can factor it out:

$(x+y)\frac{(x-y) + 1}{(x-y)^2 - (x-y)}$

Now, you can simplify further:

$(x+y)\frac{(x-y+1)}{(x-y)(x-y-1)}$

So, the simplified form of the expression $\frac{x+y+x^2-y^2}{x-y+x^2-2xy+y^2}$ is $(x+y)\frac{(x-y+1)}{(x-y)(x-y-1)}$.