To day we shall discourse on a lesson binomials operation in denominator.Binomials are variables with a number with letter separated with either additional sign ( + ) or subtraction sign ( - ) used for solving quadratic equations. Example of binomials variables can be expressed as ( d + 3) / d + 3 and (a + 2) / a + 2. Also, 2(p + 4) etc..
In this case we will take a look the operations that involved factors with binomials in the denominator,our target is the possible denominator .This mathematics need concentration and focus..
Example 1
Solve the equation 5
---------- = 2
x - 3
Note, there is only one denominator in the equation, x - 3, that whole of binomial is the denominator,it is not possible to expand it.Multiply both sides by (x - 3)
1 5
1
On the LHS ( left hand side), the ( x - 3 )s divided , leaving 5 ,then clear bracket on the RHS(right hand side).
5 = 2( x - 3 ) ---- 2x - 6
5 = 2x - 6 add six to both sides
5 + 6 = 2x - 6 + 6
11 = 2x
Divide both sides by 2 ( 2 not 2x)
1
11 2x
------ = ------
2 2
1
1
x = 5 ------
2
The main key to this mathematics is being familiar with open sentences.But with my explanation,you should be able to grab the ideas behind this.
Example 2
Solve
5 4
----------- ___ -------- = 0
7e - 1 9
The only denominator here are (7e - 1) and 9.their L . C . M is 9(7e - 1). Multiply earch tern by
9(7e - 1)
5 4
9(7e - 1) x -------- __ 9(7e - 1) x ------- = 9(7e - 1) x 0
9 x 5 - 4 (7e - 1) = 0 (collect like terms 4x7e = 28e and 4 x 1 =4)
49 - 28e - 4 = 0 + 28e (subtract 28 from both sides.)
49 = 28e ( divide both sides by 28 not 28e.)
7 1
------- = ---------
4
7 1
--------- = 1 ------
4 4
With my explanation you should understand the concept based on this math.
Example 3
solve this binomial equation.
4 3
--------- + --------- = 0
w + 3 w + 2
The L. C. M are (w + 3)(w + 2).Now multiply each term by (w + 3)(w + 2)
4 3
0 x (w + 3)(w + 2)
4 (w + 2) + 3 (w + 3) = 0 clear the brackets
4w + 8 + 3w + 9 = 0
Collect like terms.
4w + 3w 8+ 9 = 0
7w + 17 = 0
subtract 17 from bod sides.
7w + 17 - 17 = 0 - 17
7w = - 17
Divide both sides by 7 (7 not 7w)
7w -17
---------- = ------------
7 7
3
w 2-------
7
Like i said before, this mathematics need open sentences experience.
Example 3
3 2
--------- = --------
y y - 5
The L.C.M are y and y - 5 only.Multiply both sides by y(y - 5).
3 2
3(y - 5) = y x 2
3y - 15 = 2y (collect like term)
3y - 2y = 15
y = 15
In mathematics like this especially algebra, any after = the number will change sign.I mean t + 23 = 3r,the 3r will change the sign when collected like terms to -3r, because previously it is positive.Te same thing with a number before =, when such variables would go for an operation its changes.
That was amazing operation,it is very very simple to understand thing needed.I think with all the explanation you can do yours.To become a good mathematics student, you must work on math every day at least give yourself 4 good hours for practice.
Now solve the following equations
2c + 3 2
i. ----------- = --------
2c - 3 5
1 3
ii. ---------- = --------
a + 2 a + 1
1 2
iii. -------- + -------------
2v v - 25
Please if you have questions put them in the comments box.
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