0.10. Көрсетілген амалды орындаңдар: 1) x/(x−y)+y/(y−x); 2) (2x+1)/a + (3x+1)/a − (x−2)/a; 3) a/(12m) − b/(18n); 4) 3xy/(4mn) · 10m²n²/(21x²y); 5) (−18a²b²)/(5pq) : (6ab)/(5p²q²); 6) (x²y−4y³)/(3xy²) − (yx²)/(x²−2xy).

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Accepted Answer

\(\frac{x}{x-y}+\frac{y}{y-x}=\frac{x}{x-y}-\frac{y}{x-y}=\frac{x-y}{x-y}=1\), \(x\ne y\).
\(\frac{2x+1}{a}+\frac{3x+1}{a}-\frac{x-2}{a}=\frac{2x+1+3x+1-x+2}{a}=\frac{4x+4}{a}=\frac{4(x+1)}a\).
Ортақ бөлім \(36mn\): \(\frac{a}{12m}-\frac{b}{18n}=\frac{3an-2bm}{36mn}\).
\(\frac{3xy}{4mn}\cdot\frac{10m^2n^2}{21x^2y}=\frac{5mn}{14x}\).
\(\frac{-18a^2b^2}{5pq}:\frac{6ab}{5p^2q^2}=\frac{-18a^2b^2}{5pq}\cdot\frac{5p^2q^2}{6ab}=-3abpq\).
\(\frac{x^2y-4y^3}{3xy^2}-\frac{yx^2}{x^2-2xy}=\frac{y(x-2y)(x+2y)}{3xy^2}-\frac{yx^2}{x(x-2y)}=\frac{(x-2y)(x+2y)}{3xy}-\frac{xy}{x-2y}\). Ортақ бөлімге келтіргенде: \(\frac{(x-2y)^2(x+2y)-3x^2y^2}{3xy(x-2y)}\).

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