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 to lowest term or simplest form.
The following steps ill be useful to simple rational expressions.
Step 1 :
Factor both numerator and denominator, if possible.
Step 2 :
Identify the common factors in both numerator and denominator.
Step 3 :
Remove the common factors found in both numerator and denominator.
The above four steps have been illustrated in the picture given below.
Practice Questions
Question 1 :
Simplify :
4x3 / 8x2
Answer :
= 4x3 / 8x2
= (1/2)x3-2
= (1/2)x
= x/2
Question 2 :
Simplify :
(5x + 20) / (7x + 28)
Answer :
= (5x + 20) / (7x + 28)
= 5(x + 4) / 7(x + 4)
= 5/7
Question 3 :
Simplify :
(3x + 9) / (3x + 15)
Answer :
= (3x + 9) / (3x + 15)
= 3(x + 3) / 3( x + 5)
= (x + 3) / (x + 5)
Question 4 :
Simplify :
(9x2 - 25y2) / (3x2 - 5xy)
Answer :
= (9x2 - 25y2) / (3x2 - 5xy)
= [(3x)2 - (5y)2] / x(3x - 5y)
= [(3x + 5y)(3x - 5y)] / x(3x - 5y)
= (3x + 5y) / x
Question 5 :
Simplify :
(6x2 - 54) / (x2 + 7x + 12)
Answer :
= (6x2 - 54) / (x2 + 7x + 12)
= 6(x2 - 9) / (x + 3)(x + 4)
= 6(x2 - 32) / (x + 3)(x + 4)
= 6(x + 3)(x - 3) / (x + 3)(x + 4)
= 6(x - 3) / (x + 4)
Question 6 :
Simplify :
(64a3 + 125b3) / (4a2b + 5ab2)
Answer :
= (64a3 + 125b3) / (4a2b + 5ab2)
= [(4a)3 + (5b)3] / ab(4a + 5b)
= (4a + 5b)[(4a)2 - (4a)(5b) + (5b)2] / ab(4a + 5b)
= (16a2 - 20ab + 25b2) / ab
Question 7 :
Simplify :
(x2 + 7x + 10) / (x2 - 4)
Answer :
= (x2 + 7x + 10) / (x2 - 4)
= (x + 5)(x + 2) / (x2 - 22)
= (x + 5)(x + 2) / (x + 2)(x - 2)
= (x + 5) / (x - 2)
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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
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
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Ratio and proportion 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
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