Advice 1: How to solve equations with fractions

Equations with fractions - a special kind of equations have their own specific features and subtle highlights. Let's try to understand them.
How to solve equations with fractions
Instruction
1
Perhaps the most obvious point here is, of course, the denominator. Numerical fractions do not represent any danger (fractional equations where all denominators are only numbers, will generally be linear), but if the denominator is a variable, then it must be considered and administered. First, it means that the value of x, converting 0 in the denominator, the root can not be, and generally need to separately register the fact that x can't equal this number. Even if you have that if you substitute in the numerator of all perfectly convergent and satisfies the conditions. Second, we can't multiply or divide both sides of the expression equal to zero.
2
After that, the solution of this equation is reduced to the transfer of all of its members in the left part to the right remains 0.

You need to bring all members to a common denominator, domnain, where necessary, the missing numerator of the expression.
Then solve the normal equation, written in the numerator. Can make General the multipliers of the brackets, apply the formulas of reduced multiplication to cause a similar to calculate roots of a quadratic equation using the discriminant, etc.
3
The result should be factorization into a product of parentheses (x-(i-th root)). This also includes polynomials with no roots, e.g. square trinomial with a discriminant that is less than zero (unless, of course, the problem is to find only real roots, as often happens).
Definitely need to factorize the denominator to find there brackets already present in the numerator. If the denominator of expressions like (x-(number)), it is best when bringing to a common denominator standing there brackets to multiply "in a forehead", and to leave the product source of simple expressions.
The same brackets in the numerator and denominator can be reduced by writing in advance, as mentioned above, the conditions.
The answer is written in brackets how many values of x, or simply by enumeration: x1=..., x2=..., etc.

Advice 2: How to solve problems with improper fractions

A fraction is a mathematical notation of simple rational numbers. It is a number that consists of one or more fractions of a unit can be either in decimal and ordinary form. Today operations convert fractions are of great importance not only in mathematics but also in other fields of knowledge.
How to solve problems with improper fractions
Instruction
1
Typically, the most common fractions are wrong, and in this case they require specific action on the part of someone who decides examples and tasks with this fraction.
2
Take the tutorial to the task. Please read condition, reading it several times and go to solution. Let's see which fractions are to be solved action. This can be incorrect, correct or decimal fraction. Put the correct fractions in the wrong, but remember that to record all response actions will have to run back, already converting improper fraction to the correct. At common fraction the number above the fraction bar (the numerator) is always greater than the number below the line is denominator. To make the translation from proper fractions to improper follow the next steps.
3
Multiply the denominator by the integer and add the result to the numerator. For example, if a fraction of 2 integers 7/9, 9 must be multiplied by 2 and then add 7 to 18 - the end result will be 25/9.
4
Perform all necessary actions according to the task (addition, subtraction, division, multiplication) using the transformed fraction.Take your answer, it will need to be present in the fractions. To do this, divide the numerator by the denominator. For example, if you have to take the number 25/9 in a proper fraction, divide 25 by 9. As 25 9 not evenly divided, the answer is 2 and as many as seven (numerator) ninth (denominator). Now obtained the proper fraction, where the numerator more than the denominator and a part of it.
5
Record the response task correct fraction. Check your action, if it requires the condition to do task or teacher.
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