دانلود اپلیکیشن
حاصل هر عبارت را به ساده ترین صورت بنویسید. (مخرج همهٔ کسرها مخالف صفر فرض شده است.)
\(\frac{{n - \frac{{{n^2}}}{{n - m}}}}{{1 + \frac{{{m^2}}}{{{n^2} - {m^2}}}}} = \) الف
\(\frac{{\frac{y}{{x + y}} - \frac{x}{{x - y}}}}{{\frac{x}{{x + y}} + \frac{y}{{x - y}}}} = \) ب
\(\frac{{n - \frac{{{n^2}}}{{n - m}}}}{{1 + \frac{{{m^2}}}{{{n^2} - {m^2}}}}} = \frac{{\frac{{{n^2} - nm - {n^2}}}{{n - m}}}}{{\frac{{{n^2} - {m^2} + {m^2}}}{{{n^2} - {m^2}}}}} = \) الف
\(\begin{array}{l}\frac{{\frac{{ - nm}}{{n - m}}}}{{\frac{{{n^2}}}{{{n^2} - {m^2}}}}} = \frac{{ - nm}}{{n - m}} \div \frac{{{n^2}}}{{{n^2} - {m^2}}} = \\\\\frac{{ - nm}}{{n - m}} \times \frac{{{n^2} - {m^2}}}{{{n^2}}} = \\\\\frac{{ - nm}}{{n - m}} \times \frac{{(n - m)(n + m)}}{{{n^2}}} = \\\\\frac{{ - m(n + m)}}{n}\end{array}\)
\(\frac{{\frac{y}{{x + y}} - \frac{x}{{x - y}}}}{{\frac{x}{{x + y}} + \frac{y}{{x - y}}}} = \frac{{\frac{{xy - {y^2} - {x^2} - xy}}{{(x + y)(x - y)}}}}{{\frac{{{x^2} - xy + xy + {y^2}}}{{(x + y)(x - y)}}}} = \) ب
\(\begin{array}{l}\frac{{\frac{{ - {y^2} - {x^2}}}{{(x + y)(x - y)}}}}{{\frac{{{x^2} + {y^2}}}{{(x + y)(x - y)}}}} = \frac{{\frac{{ - ({y^2} + {x^2})}}{{(x + y)(x - y)}}}}{{\frac{{{x^2} + {y^2}}}{{(x + y)(x - y)}}}} = \\\\\frac{{ - ({y^2} + {x^2})}}{{(x + y)(x - y)}} \div \frac{{{x^2} + {y^2}}}{{(x + y)(x - y)}} = \\\\\frac{{ - ({y^2} + {x^2})}}{{(x + y)(x - y)}} \times \frac{{(x + y)(x - y)}}{{{x^2} + {y^2}}} = \\\\\frac{{ - ({y^2} + {x^2})}}{{{y^2} + x}} = \frac{{ - 1}}{1} = - 1\end{array}\)
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