Алгебраическая дробь — это выражение вида <span> <span>РQ</span> </span><span>, где </span>
<span>Р </span><span> и </span><span> Q </span><span> — многочлены; </span><span> Р </span><span> — числитель, а </span><span> Q </span><span> — знаменатель </span>
<span>алгебраической дроби. </span>
<span> Например: </span>
<span> <span><span>a−b</span><span><span>b 2</span>−1</span></span> </span><span> где </span><span> P = <span>a−b</span> </span><span>, </span><span> а </span><span> Q = <span><span>b 2</span>−1</span> </span><span>; </span>
<span> <span><span><span>x 2</span>+3</span><span><span>y 3</span>+x</span></span> </span><span> где </span><span> P = <span><span>x 2</span>+3</span> </span><span>, </span><span> а </span><span> Q = <span><span>y 3</span>+x</span> </span><span>; </span>
<span> <span><span><span>y 2</span>−1</span><span>y−1</span></span> </span><span> где </span><span> P = <span><span>y 2</span>−1</span> </span><span>, </span><span> а </span><span> Q = <span>y−1</span> </span><span>. </span>
<span> Многочлен — это частный случай алгебраической дроби. </span>
<span> Например, многочлен </span><span> <span><span><span>y 3</span>+<span>2y</span></span>+7</span> </span><span> равен дроби </span><span> <span><span><span><span>y 3</span>+<span>2y</span></span>+7</span>1</span> </span><span>, </span>
<span>а дробь </span><span> <span><span><span><span>3<span>x 2</span></span>+<span>5x</span></span>−1</span>5</span> </span><span> можно записать в виде многочлена </span><span> <span><span><span><span>35</span><span>x 2</span></span>+x</span>− <span>15</span></span> </span><span>. </span>
5x^2(3x-x^7) = 5x^2*x(3 - x^6) =
= 5x^3(3 - x^6)