To simplify fractional rational expression, it is necessary to make arithmetic actions in a certain order. At first operations in brackets, then multiplication and division and in the last turn – addition and subtraction are performed. The numerator and a denominator of initial fractions usually display on multipliers since during the solution of an example they can be reduced.
Instruction
1. examples/strong of"" class= "" colorbox imagefield imagefield-imagelink" of" rel= "" gallery-step-images""> At addition or subtraction of fractions, reduce them to a common denominator. For this purpose at first find a least common multiple of coefficients of denominators. It is equal in this example to 12. Calculate expression for a common denominator. Here: 12xy². Divide a common denominator into each of denominators of fractions. 12xy²: 4y²=3x and 12xy²: 3xy=4y.
2. The received expressions are additional multipliers for the first and second fractions respectively. Increase numerator and a denominator of everyone fraction. In this example receive: (3x²+20y) / 4xy³.
3. To put fractional expression and an integer, present an integer in the fraction form. The denominator can be any. For example, 4=4∙a²/a²; y=y∙5b/5b, etc.
4. To put fractions with a polynomial in a denominator, at first factorize a denominator. So, for this example, a denominator of the first fraction ax–x²=x (a–x). Execute movement in a denominator of the second fraction: x–a=–(a–x). Reduce fractions to a common denominator x (a–x). In numerator you receive expression of a²-x². Factorize its a²-x²= (a–x) (a+x). Reduce fraction on a–x. Receive in the answer: a+x.
5. To increase one fraction by another, multiply among themselves numerators and denominators of fractions. So, in this example receive y numerator² (x²–xy) and yx denominator. Put outside brackets the general multiplier in numerator: y² (x²–xy) =y²x (x–y). Reduce fraction by yx, as a result receive y (x–y).
6. To divide one fractional expression into another, increase numerator of the first fraction by a denominator of the second. In an example: 6 (m+3)² (m²–4). Write down this expression in numerator. Increase a denominator of the first fraction by numerator of the second: (2m–4) (3m+9). Write down this expression in a denominator. Factorize the received polynomials: 6 (m+3)² (m²–4) =6 (m+3) (m+3) (m–2) (m+2) and (2m–4) (3m+9) =2 (m–2)3 (m+3) of =6 (m–2) (m+3). Reduce fraction by 6 (m–2) (m+3). Receive: (m+3) (m+2) of =m²+3m+2m+6=m²+5m+6.