Definition of computing rational expressions:
A rational expression is simplified, or reduced to lowest terms, if its numerator and denominator have no common factors other than 1 and -1. If a rational expression does contain common factors, we use the properties of the real number system to write
`ac/bc`=`a/b``xx``c/c`=`a/b``xx`1=`a/b` (a, b, c are real number, and bc`!=`0.)
This process is often called “canceling common factors.” To indicate this process, we often write
`a/b`=`a/b`
Rules for Computing Rational Expressions:
Rule 1: Steps for computing rational expressions
Step 1: Set the terms containing the identical variable collectively in algebraic exponential expressions.
Step 2: Accomplish the operation inside the parentheses for the variable and other.
Step 3: Revise the rational expressions and to simplifying rational expressions.
Step 4: To make sure rational expressions, if there is able to simplify rational expressions and then repeat the step 1 to 4.
Rule 2: Order of operation for computing rational expressions
In long math problems with +,-,x,%,(), and exponents in them, you have to identify what to do first. Without follow the similar rules, you may get unlike answers. You can easily keep in mind the silly sentence, Big Elephants Destroy Mice And Snails, you can commit to memory the order of operations, and you must follow.
Big “B” means Brackets. We need to carry out operation in side parentheses first.
Elephants “E” means an exponent; you must calculate exponents next in expressions by j.
Destroy “D” means division
Mice “M” means multiply begin on the left of the equation and perform all divisions and multiplication in the order in which they appear.
And “A” means addition
Snails “S” means subtract. For all time on the left hand side and accomplish additions and subtractions operation.
Rule 3: study for computing rational expressions with exponents.
The rules are given by
`x^m` `xx` `x^n` = `x^(m+n)`
`((x^(m))/(x^(n)))` = `x^(m-n)`
`((x^(m))^n)` = `x^(mn)`
`(x y)^m` = `x^m` `y^m`
`(x/y)^n` = `(x^(n))/(y^(n))`
`x^(-n)` = `1/(x^(n))`
`(x/y)^(-n)` = `(y/x)^(n)`
Where quantities in the denominator are taken to be nonzero in computing rational expressions, Special cases include
`x^1`=`x`
And
`x^0=1`
For x`!=`0. The definition `0^o`=1 is sometimes used to simplify formulas, but it should be kept in mind that this equality is a definition and not a fundamental mathematical truth.
Example Problem for Computing Rational Expressions:
To solving computing rational expressions using above rules, ( 8`V^(2)` `-:``2V)+5`Y^(2)``xx``Y^(4)`
Solution:
Step 1: Is to group like terms. Set the terms containing the same variable jointly. Set constants collectively and brackets.
( 8`V^(2)` `-:``2V)+5`Y^(2)``xx``Y^(4)`
Step 2: Is to accomplish the operation inside the parentheses for the variable V.
( 8`V^(2)` `-:``2V)=(8`-:`2)`xx``(V^(2)``-:`V^(1))`=(`8/2`)`xx``(V^(2-1))`=4`xx``V^(1)`=4V
Step 3: Is to accomplish the operation inside the parentheses for the variable Y using expression with exponents rule.
5`Y^(2)``xx``Y^(4)`=5`xx``(Y^(2+4))`=5`xx``Y^(6)`=5`Y^(6)`
Step 4: Is to revise the given problem.
4V+5`Y^(6)`
Since the left over terms are not like terms, the problem cannot be any further.
The answer is 4V+5`Y^(6)`
A rational expression is simplified, or reduced to lowest terms, if its numerator and denominator have no common factors other than 1 and -1. If a rational expression does contain common factors, we use the properties of the real number system to write
`ac/bc`=`a/b``xx``c/c`=`a/b``xx`1=`a/b` (a, b, c are real number, and bc`!=`0.)
This process is often called “canceling common factors.” To indicate this process, we often write
`a/b`=`a/b`
Rules for Computing Rational Expressions:
Rule 1: Steps for computing rational expressions
Step 1: Set the terms containing the identical variable collectively in algebraic exponential expressions.
Step 2: Accomplish the operation inside the parentheses for the variable and other.
Step 3: Revise the rational expressions and to simplifying rational expressions.
Step 4: To make sure rational expressions, if there is able to simplify rational expressions and then repeat the step 1 to 4.
Rule 2: Order of operation for computing rational expressions
In long math problems with +,-,x,%,(), and exponents in them, you have to identify what to do first. Without follow the similar rules, you may get unlike answers. You can easily keep in mind the silly sentence, Big Elephants Destroy Mice And Snails, you can commit to memory the order of operations, and you must follow.
Big “B” means Brackets. We need to carry out operation in side parentheses first.
Elephants “E” means an exponent; you must calculate exponents next in expressions by j.
Destroy “D” means division
Mice “M” means multiply begin on the left of the equation and perform all divisions and multiplication in the order in which they appear.
And “A” means addition
Snails “S” means subtract. For all time on the left hand side and accomplish additions and subtractions operation.
Rule 3: study for computing rational expressions with exponents.
The rules are given by
`x^m` `xx` `x^n` = `x^(m+n)`
`((x^(m))/(x^(n)))` = `x^(m-n)`
`((x^(m))^n)` = `x^(mn)`
`(x y)^m` = `x^m` `y^m`
`(x/y)^n` = `(x^(n))/(y^(n))`
`x^(-n)` = `1/(x^(n))`
`(x/y)^(-n)` = `(y/x)^(n)`
Where quantities in the denominator are taken to be nonzero in computing rational expressions, Special cases include
`x^1`=`x`
And
`x^0=1`
For x`!=`0. The definition `0^o`=1 is sometimes used to simplify formulas, but it should be kept in mind that this equality is a definition and not a fundamental mathematical truth.
Example Problem for Computing Rational Expressions:
To solving computing rational expressions using above rules, ( 8`V^(2)` `-:``2V)+5`Y^(2)``xx``Y^(4)`
Solution:
Step 1: Is to group like terms. Set the terms containing the same variable jointly. Set constants collectively and brackets.
( 8`V^(2)` `-:``2V)+5`Y^(2)``xx``Y^(4)`
Step 2: Is to accomplish the operation inside the parentheses for the variable V.
( 8`V^(2)` `-:``2V)=(8`-:`2)`xx``(V^(2)``-:`V^(1))`=(`8/2`)`xx``(V^(2-1))`=4`xx``V^(1)`=4V
Step 3: Is to accomplish the operation inside the parentheses for the variable Y using expression with exponents rule.
5`Y^(2)``xx``Y^(4)`=5`xx``(Y^(2+4))`=5`xx``Y^(6)`=5`Y^(6)`
Step 4: Is to revise the given problem.
4V+5`Y^(6)`
Since the left over terms are not like terms, the problem cannot be any further.
The answer is 4V+5`Y^(6)`
