Да се извършат означените операции.

[FlashTerran]

1.
[tex](\frac{m-n}{mn } -\frac{3m+n}{mn-m^{2} }+\frac{3n+m}{ mn-n^{2}} ):\frac{2m+2n}{ mn}+\frac{2m}{ n-m} [/tex]
2.
J=[tex]\frac{b}{ x-b}-\frac{ab}{ x-a}(\frac{x+a}{ax-ab }+\frac{x+b}{ b^{2}-bx}+\frac{x}{ ab} [/tex]

Моля,помагайте.

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[Spider Iovkov]

[tex]\frac{b}{x-b}-\frac{ab}{x-a}(\frac{x+a}{ax-ab}+\frac{x+b}{b^2-bx}+\frac{x}{ab})=\\=\frac{b}{x-b}-\frac{ab}{x-a}(\frac{x+a}{a(x-b)}+\frac{x+b}{b(b-x)}+\frac{x}{ab})=\\=\frac{b}{x-b}-\frac{ab}{x-a}(\frac{x+a}{a(x-b)}-\frac{x+b}{b(x-b)}+\frac{x}{ab})=\\=\frac{b}{x-b}-\frac{ab}{x-a}(\frac{bx+\cancel {ab}-ax-\cancel {ab}}{ab(x-b)}+\frac{x}{ab})=\\=\frac{b}{x-b}-\frac{ab}{x-a}.\frac{bx-ax+x(x-b)}{ab(x-b)}=\\=\frac{b}{x-b}-\frac{ab}{x-a}.\frac{\cancel {bx}-ax+x^2-\cancel {bx}}{ab(x-b)}=\\=\frac{b}{x-b}-\frac{\cancel {ab}}{\cancel {x-a}}.\frac{x\cancel {(x-a)}}{\cancel {ab}(x-b)}=\\=\frac{b}{x-b}-\frac{x}{x-b}=\\=\frac{-(x-b)}{x-b}=\\=-1; a\neq 0, b\neq 0, x\neq a, x\neq b[/tex]

[FlashTerran]