How to solve rational equation

Introduction:

Solving rational equations is one of the important topics that we need to know. What we do to one side of the equation, must do to the other. If we have fractions, we try to eliminate them by multiplying by the common denominator. Suppose, If there are quadratics involved, we must get all terms to one side with zero on the another.

Steps involved in solving a rational equation

Solving rational equation is an important to see at an equation that not having a variable in the denominator to make confident that we see the pattern for calculating rational equations. The following steps we will use in the solution process.

1. First we need to determine the least common denominator of the fractions in the given rational equation.

2. We need to take out the fractions by multiplying All terms by the least common denominator.

3. Then we have to simplify the terms in rational equation.

4. Solve the resulting equation.

5. Check the answers to make confident the solution does not make the fraction undefined.

Let’s look at first, how we would handle the equations like x/3 + 2x/2 = 4

Our first step in solving this equation is to multiply each term by its least common denominator of the fractions, which is 6

(6) x/3 + (6) 3x/2 = (6) 4

Simplifying the above equation results in the linear equation which we can solve to get our final answer.

2x + 6x = 24

8x = 24

x = 3

Hope you like the above explanation. Please leave your comments, if you have any doubts.

Solve absolute value inequalities

Introduction:

        Other than algebra, there is one more important inequality. It is called as Absolute value inequality. The absolute value for any number is numerical value regardless of its sign.  For example, the absolute value of | -5 | is 5 and │+5 │ is 5. Here the vertical lines denotes absolute value.

It is a little more difficult when dealing with equations. There are three possible outcomes for absolute value inequalities. 

1. If x is any expression and a any positive number, and │x │= a, then it has either x = a or x = - a values.
2. If x is any expression and a any positive number, and │x │<>
3. If x is any expression and a any positive number, and │x │> a then it looks   x < -a and x > a.

Example

Solve: │4x – 4 │ = 8

Solution:

Use the result, if |x| = a, then x = a or x = -a

Here │4x – 4 │ = 8

So, it has either 4x – 4 = 8 or  4x – 4 = -8 values.

Solve each equation using the addition and multiplication principles.

4x = 12,    4x = -4

after solving the equation, we get

x = 3,     x = -1. Answer

Hope you like the above explanation to solve the absolute value inequalities, Please leave your comments, if you have any doubts.

Practice of Algebra Application

Introduction:

 Applications of algebra are found everywhere; the principles of algebra are applied in all branches of mathematics, for instance, calculus, geometry, and topology. They are applied every day by men and women working in all type of business. As a typical example of applying algebraic methods.

     Algebra is often referred to as a generalization of arithmetic, so it is collection of rules, then the rules for translating words into symbolic notation of mathematics, rules for formulating statements using symbolic notation, and rules for rewriting mathematical statements in  a manner that leaves their truth unchanged. 

Application of Algebra in Slopes of Straight Lines:

In general slope of equation is y=mx+b
Practice  Problem 1:
Y=x-3
Where m=1 (co efficient of x)
               B=-3
Equation of point-slope :
 Formula for point,slope
                (y-y1)=m(x-x1)

Practice  problem 1.  Find the equation of the line which passes through the point (2, 2) and has slope3.
Solution:
       Equation is    (y-y1)=m(x-x1)
Where, x1=2
                Y1=2
                M=3
So,
        y-2=3(x-2)
        y-2=3x-6
Answer is: 3x-y-4=0

Learn factor polynomials calculator

Introduction:

         Calculator is used to solve different types of problems. It is a web-based tool designed to solve different problems. Learning factor polynomials through calculators is simple. 

      Factor polynomials calculator are used to understand the polynomials factorization. Given expression can be factorized by using the greatest common factor. Let us discuss about the learn factor polynomials calculator.

Steps to learn factor polynomials:

The Steps to learn factor polynomials are as follows:

• Given expression can be arranged in the order of powers.
• Expression can be in the form of standard ax² + bx + c = 0.
• The expression should be factorized.
• Solve the given terms.

Example problems to learn factor polynomials calculator:

Factorize: 42ax + 36bx – 7ax²– 6by² using factor by group
Solution:
Step 1:
          Given expression 42ax + 36bx – 7ax²– 6by²
Step 2:
           Given expression in the standard form ax² + bx + c = 0
                     42ax + 36by – 7ax²– 6by² = 0
Step 3:
           Groups the terms
                      42ax – 7ax² +36by – 6by² = 0
                      7ax (6 – x) + 6by (6 – y) = 0
Step 4:
           The greatest common factor for the expression
                      7ax (6 – x) + 6by (6 – y) = 0
                     (7ax + 6by) (6 – x) (6 – y) = 0
Solution to the given equation is (5a – 6x) (3b – 4y) (b – 3y) = 0.

Hope you like the above explanation, Please leave your comments, if you have any doubts.

About Polynomials

Introduction:

           An algebraic expression in which the variables have only non negative powers is called polynomial.  The monomial midterm study which contains finite number sum in x it said to be polynomial. The coefficients of the polynomial are said to be coefficients of the monomial in a polynomial. If coefficients of a polynomial are zero, then polynomial is said to be  zero polynomial. The highest coefficient power of x in a polynomial is called the leading coefficient for polynomial

Fundamental of Polynomial

Constants and variables are the fundamentals of polynomials.
Examples :In the formula for circumference of a circle, c=2π r ² and π are constants and c and r are variables

Degree and Types of Polynomials

Polynomials with more than one variable, the sum of powers of the variables taken up and the highest sum so obtained is called the degree of the polynomial.
Monomial, Binomial and Trinomials are three different types of Polynomials.

Properties of Polynomials

Addition and subtraction of two polynomials mean combining like terms.
We can perform multiplication and division also

Factorization of Polynomials

     You know that any polynomial of the form p(a) can also be written as
p(a) = g(a) x h(a) + R(a) it implies that Dividend = Quotient X Divisor + Remainder.
If the remainder is zero, then p(a) = g(a) x h(a). That is, the polynomial p(a) is a product of two other polynomials g(a) and h(a).

Order of operation using algebra

Introduction of order of operation using algebra:
 The Order of Operation using algebra is
P          - Parentheses,
E          - Exponents,
M         - Multiplication,
D          - Division,
A          - Addition and
S          - Subtraction

1. Calculations have to be finished from left to right in algebra.
2. First complete the operations inside a parenthesis.
3. Next Complete the operations of  exponents.
4. Then do multiplication and division, from left to right.
5. Then  do addition and subtraction, from left to right.

Step by step process for order of operation:

Parenthesis

                In algebra the parenthesis, combining symbols are always completed from the innermost set outward.

Exponents

                In algebra, an exponent is unlike than just multiplying. 

Example: 2^4 means 2 x 2 x 2 x 2 = 16

Evaluate 2 + 5 x (4 + 3) ÷ 2 - 6 using the order of operations.

Solution: 

Step 1:	2 + 5 x (4 + 3) ÷ 5 - 6	=	2 + 2 x 9 ÷ 3 – 6	Parentheses
Step 2:	2 + 5 x 7 ÷ 5 – 6	=	2 + 18 ÷ 3 – 6	Multiplication
Step 3:	2 + 35 ÷ 5 – 6	=	2 + 6 – 6	Division
Step 4:	2 + 7 - 7	=	2+6 – 6	Addition
Step 5:	2	=	2	Subtraction

Multiplication and Division in algebra

                These operations are completed in the order they show from left to right.  They are finished together because they have same importance.

Addition and Subtraction in algebra

         These two operation have two operations of the same importance. These are finished in the order that they show from left to right. 

Hope you like the above explanation, Please leave your comments, if you have any doubts.

Learn Greatest Common Factor

Introduction:
        Greatest Common Factor (GCF) is the greatest number that is a factor of each of two or more numbers. To find either the Least Common Multiple (LCM) or Greatest Common Factor (GCF) of two numbers, you always start out the same way: you find the prime factorizations of the two numbers. Then you put the factors into a nice neat grid of rows and columns, and compare and contrast and take what you need.
Let us study the GCF of two numbers 24 and 15.
The factors of 24 are 1,2,3,4,6,8,12 and 24.
The factors of 15 are 1,3,5 and 15.
From this we observe that the greatest factor common to both these numbers are 3. In other words we can say that the greatest common factor of 24 and 15 is 3.

Greatest Common Factor Learning

Another method of finding out  the GCF is by using prime factorisation. The prime factors of 8 are 1,2,2,2 and that of 12 are 1,2,2,3. The prime factors that is  common for both numbers are 1,2,2. Multiply together all these numbers and we get 4. We can say that 4 is the greatest common factor of these numbers.