I will show you how to calculate algebraic fractions operation.If you are an SS2 (Senior class) you have bring your your attention about this particular lesson.
Well.i promised to explain them to your understanding. In mathematics, an algebraic fractions whose denominator is equal to zero is said to be undefined.Lt look at some variables that is involve in this matter.
For example
1
--------
x + 2
This is to say that x = -2 fractions
We can also consider these as an undefined algebraic fractions
1 1 1
------- = -------- = -------
x + 2 (-2)+2 0
It is obvious that that division with zero is impossible in mathematics operations. When the value of x approaches 2, the value of the functions:
4
-------
x + 2
It is then said that ,the value of x range from
-3/4 to +7
To make it clear to you view,when you have minus sign(-) you are to replace it with plus sign(+)The same with plus to minus.Now,let look at some examples and how to deal with them.
Example 1
Find the value of x for which each of the following algebraic fractions is undefined:
5
(a) --------
2x + 4
this is undefined when 2x + 4 is zero (0)
if 2x + 4 = 0
2(x + 2) = 0
x + 2 = 0 or x = -2
It is undefined when
x = -2
7
(b) --------------- This is undefined when
( x - 3)( x - 2)
(x - 3)( x - 2) = 0
if (x - 3)( x - 2) = 0,
then x - 3 =0 or x - 2 =0
Therefore the fraction is undefined when
x = 2 (not +2) or x = 3
2(x - 1)
(c) ---------------
x² -25
The above is This is undefined when
x² -25
if x² -25 =0,
take the square root
x² - 5²
then ( x + 5)( x - 5) = 0
either x + 5 = 0 or x - 5 = 0
x = -5 or x = 5
The is a fraction with undefined when x = -3 or 3.
x + 3
(d) -------------
x² - 3x - 10
x² - 5x - 10 = 0
Now, look for the same number that when you add it will give you - 3 and the same number when you multiply it will give you -10,these numbers are -5 + 2 and -5 x (+2)
if x² - 5x - 10 = 0
x² - 5x + 2x - 10 = 0
x( x - 5 ) + 2 ( x - 5 ) = 0 --- 10/2
( x - 5 )(x + 2 ) = 0
either x - 5 = 0 , x + 2 = 0
x = 5 or x = - 2
Therefore the fraction is undefined when x = 5 or x = - 2
The above operation can only be done if you are familiar with factorization method and the inverse rules.
(e) What is the value of x in this.
3
--------- this undefined fraction
x - 6
if x - 6 =0
then x + 6 = 0 or x = - 6 or 0.
The above operation can only be done if you are familiar with factorization method and the inverse rules.
Example 2
What value (s) of is the expressi
3y + 12
(a) --------------
y² + y - 20
Solution
The expression is undefined when its denominator y² + y - 20
This is undefined when its denominator y² + y - 20 =0 ------ the single y is 1 (one)
y² + y - 20
Find two numbers that when adding you have 1 and when you multiply you have - 20, they are +5 -4 =1
and -5 x (+4) - = -20
y² + 5v - 4y - 20 = 0
y(y + 5y) - 4 ( y +5) = 0
(y - 4)(y + 5) =0
either y -4 = 0 / y + 5 = 0
y = 4/ y = -5
(b) You may be asked to find the value (y ) of the numerator expression is zero when the algebraic expression is zero.
3y + 12
----------------
y² + y - 20
3y + 12 = 0
3y = 0 - 12
3y = - 12
Divide both sides by 3 (not 3y)
3y - 12
------- = ---------
3 3
y = - 4
We said this will be zero when y = -4
(c) Fine the value of x in
x y z
------ + -------- - ------- is undefined when
x - 1 x - 2x x + 2x
(x - 1)(x - 2x) = 0
Remember, x - 2x = x - 2.
either x - 2 = 0 or x - 1
We say that the fraction is undefined when x = 1 or x = 2
Class Activities
Find the values of p in the following:
5p
(a) ----------
4p - 12
6p + 2
(b)-------------------
p² + 11p + 18p
2p - 1
(c) ------------
p
3p + 2
(d)--------------------
p(p + 3)(p + 2)
Make sur you follow the basic rules and are good to go, if there are issues you can call my number @ +2347084650763.
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