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.
Instruction
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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.
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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.
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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 equations

The solution of the equations , without which it is impossible to do in physics, mathematics, chemistry. At the very least. Learn the basics of their decision.
Instruction
1
In the most General and simple classification of the equation can be divided by the number of variables they contain and the degree in which these variables are.

To solve an equation means to find all its roots or to prove that they are not.

Any of the equations has at most P roots, where P is the maximum degree of a given equation.

But some of these roots may coincide. For example, the equation x^2+2*x+1=0, where ^ is the icon exponentiation, folded in a square of expression (x+1), that is the product of two identical brackets, each of which gives x=-1 as solutions.
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If the equation has only one unknown, it means that you will be able to explicitly find the roots (real or complex).

To do this, most likely need different transformations: formulas of reduced multiplication to the calculation formula of the discriminant and roots of a quadratic equation, the transfer of terms from one part to another, the bringing to a common denominator, multiply both sides by the same expression, squaring, etc.

Conversion, not affecting the roots of the equation are called identical. They are used to simplify the solution of the equation.

You can also instead of the traditional use of analytical graphical method and write the given equation as a function, then conducting her research.
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If the equation more than one unknown, you can only Express one of them through the other, thereby showing the set of solutions. Such, for example, equations with parameters, which contain the unknown x and the parameter a. To solve the parametric equation means for all and to Express x in a, that is, to consider all possible cases.

If in the equation are derivatives or differentials of an unknown (see picture), congratulations, it's a differential equation, and then you can not do without mathematics).
How to solve equations

Advice 3: How to solve problems with fractions

To solve the problem with fractions, you need to learn how to do arithmetic. They can be decimal, but most often uses natural fraction with the numerator and denominator. Only after that you can go to to solve math problems with fractional quantities.
You will need
  • calculator;
  • - knowledge of the properties of fractions;
  • - the ability to perform operations with fractions.
Instruction
1
The roll call record of division of one number by another. Often to do this completely is impossible, therefore, leave this step "unfinished . A number that is divisible (it is above or in front of the sign of the fraction) is called the numerator and the second number (under the sign of the fraction or after it) is the denominator. If the numerator is more than denominator, the fraction is called improper, and it is possible to allocate the integer part. If the numerator less than the denominator, such a fraction is called proper, and its integer part equal to 0.
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Tasks with fractions are divided into several types. Determine which of them is the challenge. The simplest option – finding fractions of numbers expressed in fraction. To solve this problem, it is sufficient to multiply this number by the fraction. For example, the warehouse delivered 8 tons of potatoes. In the first week, it sold 3/4 of its total. How many potatoes are left? To solve this problem, the number 8 and multiply by 3/4. Makes 8∙3/4=6 t
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If you want to find the number of parts, multiply the known part of a number the inverse of that which shows what proportion of this part in the number. For example, 8 students constitute 1/3 of the total number of students. How many children are studying in class? Because 8 people is the part that is 1/3 of the total number, then find the inverse fraction, which is equal to 3/1 or just 3. Then, to obtain the number of students in class 8∙3=24 students.
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When you need to find what part number is one number from another, divide the number which represents the part on that which is whole. For example, if the distance between the cities is 300 km and the car has driven 200 km, what part of this is from all the way? Share part of the journey 200 with the complete path 300, after the reduction of the fraction will get the result. 200/300=2/3.
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To find the unknown part of the proportion of when there is known to take an integer for the standard unit, and subtract from it a certain amount. For example, if you have passed 4/7 part of the lesson, how long? Take the whole lesson as a conventional unit and subtract from it 4/7. Get 1-4/7=7/7-4/7=3/7.

Advice 4: 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.
Instruction
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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.
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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.
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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.
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Record the response task correct fraction. Check your action, if it requires the condition to do task or teacher.
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