Задание 493

Решение:

• \({\largeа)}\ \frac{a^2-b^2}{a+b}=\frac{ (a+b)(a-b)}{a+b}=\frac{a-b}{1}=a-b\)

• \({\largeб)}\ \frac{x-1}{x^2-1}=\frac{x-1}{ (x+1)(x-1)}=\frac{1}{x+1}\)

• \({\largeв)}\ \frac{m^2-n^2}{2m+2n}=\frac{ (m+n)(m-n)}{ 2(m+n)}=\frac{m-n}{2}\)

• \({\largeг)}\ \frac{xm+xn}{m^2-n^2}=\frac{ x(m+n)}{ (m+n)(m-n)}=\frac{x}{m-n}\)

• \({\largeд)}\ \frac{x^2-2x+1}{x^2-1}=\frac{ (x-1)^2}{ (x+1)(x-1)}=\frac{ (x-1)(x-1)}{ (x+1)(x-1)}=\frac{x-1}{x+1}\)

• \({\largeе)}\ \frac{a^2-b^2}{b^2+2ab+a^2}=\frac{ (a+b)(a-b)}{ (a+b)^2}=\frac{ (a+b)(a-b)}{ (a+b)(a+b)}=\frac{a-b}{a+b}\)

• \({\largeж)}\ \frac{n^2-m^2}{ (n-m)^2}=\frac{ (n+m)(n-m)}{ (n-m)(n-m)}=\frac{n+m}{n-m}\)

• \({\largeз)}\ \frac{p-p^2}{p^2-1}=\frac{ p(1-p)}{ (p+1)(p-1)}={-}\frac{ p(p-1)}{ (p+1)(p-1)}={-}\frac{p}{p+1}\)

• \({\largeи)}\ \frac{x+x^2}{x^3-x}=\frac{ x(1+x)}{ x(x^2-1)}=\frac{ x(x+1)}{ x(x+1)(x-1)}=\frac{1}{x-1}\)

• \({\largeк)}\ \frac{a^3-2a^2}{4-a^2}=\frac{ a^2(a-2)}{ (2+a)(2-a)}={-}\frac{ a^2(2-a)}{ (2+a)(2-a)}={-}\frac{a^2}{2+a}\)