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{Evaluating and simplying Rational
Expressions} |
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Team members |
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Names: Raheel Zaman
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Overview |
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To add or subtract
polynomials, students should remove brackets and
then combine the like terms. Before simplifying
the questions, student should write down the
restrictions and then simplify to the lowest
terms. In the chapter, students have to be
careful with their careless mistakes and for
that students have to look at their solutions
two or three times. If you just do few questions
for practice you will find that chapter two is
the easiest chapter in this entire book.
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Study Tips,
Methods and or Advice |
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Remove the
brackets
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Take common terms
out and reduce from numerator and denominator.
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Combine like
terms.
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Perform addition
or subtraction.
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Group like term
again.
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Sample
Questions and complete solutions |
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Questions |
Complete Solutions |
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1. Evaluate
(3y-4x²) / 6xy
when x= -1 and
y = 3
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Substitute the
values of x and y into the equation
3(3) – 4(-1) ² /
6(-1)(3) = 9 - 4(1) / -18
= 5 / -18 |
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2.For which defined
values x is the following expression
undefined.
(8x+16) / x²-25
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x²-25 has two
factors> (x+5) and (x-5) (difference of
square)
The denominator
cannot be equal to zero as the
expression will be undefined. Therefore,
(x+5) =
0 (x-5) = 0
x =
-5 x = 5
For x=5 and x=-5,
the expression will be undefined. |
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3. Simplify
(10x-10y) / 6y –
6x
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Take common
multiple out.
10 (x-y) / 6 (y-x)
= -10 (-x+y) / 6 (y-x)
Remember (-x+y) is
same as (y-x)
Therefore,
-10 (y-x) / 6
(y-x) = -10/6 = -5/3. |
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4.Simplify
(z²-7z+10) / z-5
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Factorize the
numerator
z²-5z-2z+10 / z-5 =
z (z-5)-2(z-5) / z-5
= (z-5)(z-2) /
(z-5) = z-2 |
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Extra
Practice Questions and Answers |
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Extra Practice Questions |
Answers |
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1. Evaluate
(2x²+3x-5) /
6x+1 when x=2 |
3/11 |
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2. For which values
of x is each rational expression
undefined?
a. (3-x)/
3+x b. (x²+1)/ x²-1
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a. x=3
b. x=1,x= -1 |
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3. Simplify
a.
(55m³n²) / 75 mn³
b.
(18a²) / 3a-6a³
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a. 11m²/15n
b. 6a / 1-2a² |
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4. Simplify the
following rational expressions:
a.
z-1 / 1-z
b.
(x²-1) /
(x+1)(x-1) |
a. -1
n. 1 |
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5.State
restrictions on the variables and then
simplify
(2x²+4x+2) /
(2x²-2)
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For x=1 and x=-1,
the expression is undefined.
(X+1) / (x-1) |
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Self
Reflection |
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I find rational
expressions something interesting to learn. When
I first heard the name “Rational”, I was
confused but when I actually solved a couple of
question and I found rational expression quite
easy to understand. I am actually less terrified
now from moving onto the next section. This
section helped me to understand what undefined
expressions are which will definitely help me in
grade 12 Calculus. To solve the expressions by
substituting values of (x and y) was bit
challenging because I make careless mistakes.
But after doing practice I made few errors.
Therefore the section should be studied by all
grade 11 students as it strengthens basic
mathematical skills.
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