Simplifying Expressions
In this page we are going to discuss about simplifying expressions concepts. Simplify means converting complexity into simple and then solving it. In other words breaking a problem, into simple terms or terminologies can be defined as Simplification. Students always find difficulty in simplifying problems but, its actual purpose is to break down problems into steps and then solving it. There are different ways of simplifying, and different methods followed by different tutors for simplifying expressions.
Simplify the term itself suggests that it means simplifying things. But when it comes to math, it is not that simple. Simplification is one of the major operation of math and to work out simplify problem is very difficult without having clear concept. Simplification in math is applied to different concepts and these are: simplifying radical expressions, square roots, rational expressions, fractions, exponents, algebraic expressions, complex fractions, equations and expressions.
Let's discuss the most frequently discussed topics covered in simplification and how to simplify expressions.
Simplify Radical Expressions
Radical expressions are the combination of both variables and numbers inside a root. Radical expressions should be broken into pieces in order to get its simplest form.
Example:
Simplify `1/sqrt(2)` +`1/8` = `1/sqrt(2)` +`1/(2sqrt(2))`
= `2/(2sqrt(2))` + `1/(2sqrt(2))`
=`3/(2sqrt(2))`
Simplify square roots
The process of obtaining the 'square root' of a number is termed as 'solving' or' simplification'. The number is broken down to its factors to obtain the number which satisfies the condition of being the square root of the number.
Example: Find `sqrt(48)` =`sqrt(2*2*2*2*3)` =`2*2sqrt(3)` =`sqrt(3)`
Fing `sqrt(x^(2)36)` =`sqrt(x*x*2*2*3*3)` =x*2*3 =6x
Simplify rational expressions
A rational expression is more than a fraction in which the numerator and/or the denominator are polynomials.Simplifying rational expression involve breaking down fractions.
Example:
Solve `(x^(2)+3x+2)/(x+2)` = `(x^(2)+x+2x+2)/(x+2)` = `(x(x+1)+2(x+1))/(x+2)`
= `((x+1)(x+2))/(x+2)` =x+1
Simplify fraction
Simplify fraction involves breaking a bigger fraction to smaller one, converting mixed toimproper fraction and then solving the problem.
Example:
Solve 2`2/3` -`1/3` = `8/3` - `1/3` = `7/3`
Simplify exponents
Exponentiation is a mathematical operations, written as an, involving two numbers, the base a and the exponent n.
Example:
Solve x2.x3=x2+3=x5
Solve `x^(5)/x` =x5.x-1=x5-1=x4
Simplify algebraic expressions
An Algebraic Expression is a combination of numerals, variables and arithmetic operations such as +, -, * and /.
Example:
Simplify 2x+5x-(4+5)x+7x-2
Solution: 2x+5x-(4+5)x+7x-2=2x+5x-9x+7x-2=14x-9x-2
=5x-2
Simplify complex fractions
If a fraction is composed ofnumerator and denominator as a fraction, it is called complex fractions.
Example:Solve `(3/4)/(6/8)` = `3/4` * `8/6` = `2/2` =1
Simplify equations
A number which satisfies the given equation is called a solution or root of that.‘Satisfying the equation’ means that if the variable (literal) involved in this is replaced by the number, then both sides of that become equal. Understand the basic concepts and master your subject.
Example:
Solve 2x + 3 - 6x = -7x
2x - 6x + 3 = -7x
-4x + 3 = -7x
-4x + 7x = -3
3x = -3
x = -1
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