SIMPLIFYING RATIONAL EXPRESSIONS
About "Simplifying rational expressions"
Simplifying rational expressions :
The expression which is in the form of f(x) / g(x) is called rational expression.
Simplifying rational expression is nothing but expressing the the rational expression in its lowest term or simplest form.
Simplifying rational expressions - Steps
Step 1 :
Factor both numerator and denominator, if possible.
Step 2 :
Identify the common factor at both numerator and denominator.
Step 3 :
The common factor identified at both numerator and denominator should be multiplied by the other terms.
Step 4 :
Now, get rid of the common factor at both numerator and denominator.
The above four steps have been illustrated in the picture given below.
Simplifying rational expressions - Examples
Example 1 :
Write the simplified expression for the function defined by
f(x) = 4x³ / 8x²
Solution:
In this example we have x³ and x² . We have to split these two terms as much as possible.
f(x) = 4.x.x.x / 8 x.x
Getting rid of two x's at both numerator and denominator, and simplifying 4/8, we we get
f(x) = x / 2
Example 2 :
Write the simplified expression for the function defined by
f(x) = (5x + 20) / (7x + 28)
Solution:
Factoring the numerator and denominator of the given rational function, we get
f(x) = 5(x + 4) / 7(x + 4)
Getting rid of the common factor (x + 4) at both numerator and denominator, we get
f(x) = 5 / 7
Example 3 :
Write the simplified expression for the function defined by
f(x) = (3x + 9) / (3x + 15)
Solution:
Factoring the numerator and denominator of the given rational function, we get
f(x) = 3(x + 3) / 3(x + 5)
Getting rid of the common factor 3 at both numerator and denominator, we get
f(x) = (x + 3) / (x + 5)
Example 4 :
Write the simplified expression for the function defined by
f(x) = (9x² - 25y²) / (3x² - 5xy)
Solution:
f(x) = (9x² - 25y²) / (3x² - 5xy)
f(x) = [(3x)² - (5y)²] / (3x² - 5xy)
Factoring the numerator and denominator of the given rational function, we get
f(x) = [(3x + 5y)(3x - 5y)] / x(3x - 5y)
Getting rid of the common factor (3x - 5y) at both numerator and denominator, we get
f(x) = (3x + 5y) / x
Example 5 :
Write the simplified expression for the function defined by
f(x) = (6x² - 54) / (x² + 7x + 12)
Solution:
Factoring the numerator and denominator of the given rational function, we get
f(x) = 6(x² - 9) / (x + 3)(x + 4)
f(x) = 6(x² - 3²) / (x + 3)(x + 4)
f(x) = 6(x + 3)(x - 3) / (x + 3)(x + 4)
Getting rid of the common factor (x + 3) at both numerator and denominator, we get
f(x) = 6(x-3) / (x + 4)
Example 6 :
Write the simplified expression for the function defined by
f(x) = (64a³ + 125b³) / (4a²b + 5ab²)
Solution:
f(x) = (64a³ + 125b³) / (4a²b + 5ab²)
f(x) = (4³a³ + 5³b³) / (4a²b + 5ab²)
f(x) = [(4a)³ + (5b)³] / (4a²b + 5ab²)
Factoring the numerator and denominator of the given rational function, we get
f(x) = [4a + 5b][(4a)² - 4a.5b + (5b)²] / ab(4a + 5b)
f(x) = [(4a)² - 4a.5b + (5b)²] / ab
f(x) = [16a² - 20ab + 25b²] / ab
Getting rid of the common factor (4a + 5b) at both numerator and denominator, we get
f(x) = [(4a)² - 4a.5b + (5b)²] / ab
f(x) = [16a² - 20ab + 25b²] / ab
Example 7 :
Write the simplified expression for the function defined by
f(x) = (x² + 7x + 10) / (x² - 4)
Solution:
f(x) = (x² + 7x + 10) / (x² - 4)
f(x) = (x² + 7x + 10) / (x² - 2²)
Factoring the numerator and denominator of the given rational function, we get
f(x) = (x + 2)(x + 5) / (x + 2)(x - 2)
Getting rid of the common factor (x + 5) at both numerator and denominator, we get
f(x) = (x + 5) / (x - 2)
After having gone through the stuff given above, we hope that the students would have understood "Simplifying rational expressions".
Apart from the stuff given above, if you want to know more about "Simplifying rational expressions", please click here
Apart from stuff "Simplifying rational expressions", if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Time and work word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Recent Articles
-
Formula for a Squared minus b Square
Aug 17, 19 07:24 AM
Formula for a Squared minus b Square - Example Problems and Step by Step Solutions
-
Formula for a plus b Whole Square
Aug 17, 19 06:39 AM
Formula for a plus b Whole Square - Example Problems and Step by Step Solutions
-
Formula for a minus b Whole Square
Aug 17, 19 06:35 AM
Formula for a minus b Whole Square - Example Problems and Step by Step Solutions
