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حاصل عبارت های زیر را به دست آورید.
\(\frac{{{x^2}}}{{x - y}} + \frac{{{y^2}}}{{y - x}}\) الف
\(\frac{6}{{5x}} - \frac{4}{x}\) ب
\(\frac{{2{x^2} - 16}}{{{x^2} - 4}} - \frac{{x + 4}}{{x + 2}}\) ج
\(\frac{7}{{{x^2} - x - 2}} + \frac{x}{{{x^2} + 4x + 3}}\) د
\(\frac{{{x^2}}}{{x - y}} + \frac{{{y^2}}}{{y - x}} = \frac{{{x^2}}}{{x - y}} - \frac{{{y^2}}}{{x - y}} = \) الف
\(\frac{{{x^2} - {y^2}}}{{x - y}} = \frac{{(x - y)(x + y)}}{{x - y}} = x + y\)
\(\frac{6}{{5x}} - \frac{4}{x} = \frac{6}{{5x}} - \frac{{4 \times 5}}{{5x}} = \) ب
\(\frac{{6 - 4 \times 5}}{{5x}} = \frac{{6 - 20}}{{5x}} = \frac{{ - 14}}{{5x}}\)
\(\frac{{2{x^2} - 16}}{{{x^2} - 4}} - \frac{{x + 4}}{{x + 2}} = \) ج
\(\begin{array}{l}\frac{{2{x^2} - 16}}{{{x^2} - 4}} - \frac{{(x + 4)(x - 2)}}{{(x + 2)(x - 2)}} = \\\\\frac{{2{x^2} - 16}}{{{x^2} - 4}} - \frac{{{x^2} + 2x - 8}}{{{x^2} - 4}} = \\\\\frac{{2{x^2} - 16 - ({x^2} + 2x - 8)}}{{{x^2} - 4}} = \\\\\frac{{{x^2} - 2x - 8}}{{{x^2} - 4}} = \frac{{(x - 4)(x + 2)}}{{(x - 2)(x + 2)}} = \\\\\frac{{x - 4}}{{x - 2}}\end{array}\)
\(\frac{7}{{{x^2} - x - 2}} + \frac{x}{{{x^2} + 4x + 3}} = \) د
\(\begin{array}{l}\frac{7}{{(x + 1)(x - 2)}} + \frac{x}{{(x + 1)(x + 3)}} = \\\\\frac{{7(x + 3) + x(x - 2)}}{{(x + 1)(x - 2)(x + 3)}} = \\\\\frac{{7x + 21 + {x^2} - 2x}}{{(x + 1)(x - 2)(x + 3)}} = \\\\\frac{{{x^2} + 5x + 21}}{{(x + 1)(x - 2)(x + 3)}} = \\\\\frac{{{x^2} + 5x + 21}}{{{x^3} + 2{x^2} - 5x - 6}}\end{array}\)
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