How do we solve exponential equations ?
How to solve 100 +10 ^x where the 'x' is unknown but you that 10 *10 is 100 so "x' equals 2
When the bases/ numbers are the same the exponents must be equal as well
solve for 3^x+4 = 3^7
first just set up the exponents like an equation : x+4 = 7 , the solve algebraically
x will equal =11
11 is the new exponent
Try this with ; 2 ^3x+7 = 2^5x-1
set up the exponents 3x+7 =5x-1 then solve algebraically
then end result will be that x= 4 this becomes the new exponent
Sunday, January 20, 2013
1/713 how do we solve complex fractions?
How do we solve complex fractions?
When you see a complex fraction , it usual consists of another fraction for example;
1/1/3
The first step its rewrite it as 1 divided by 1/3
Then you do the reciprocal to the "1/3" so you can turn the divisor bar into multiplication so it become 3/1 or 3
Then it becomes1*3 and the end result is 3
Try with another example :
1/1/x+1
so first write it as 1 divided by 1/x+1
then do the reciprocal to change the sign so it becomes multiplication ; 1* x+1
now multiply and your result becomes x+1
When you see a complex fraction , it usual consists of another fraction for example;
1/1/3
The first step its rewrite it as 1 divided by 1/3
Then you do the reciprocal to the "1/3" so you can turn the divisor bar into multiplication so it become 3/1 or 3
Then it becomes1*3 and the end result is 3
Try with another example :
1/1/x+1
so first write it as 1 divided by 1/x+1
then do the reciprocal to change the sign so it becomes multiplication ; 1* x+1
now multiply and your result becomes x+1
12/18/12 How do we add and subtract rational expression ?
How do we add and subtract rational expressions ?
-When adding and subtracting rational expressions, it takes the same method as adding and subtracting fractions.
Example : 4/x+8 +3/x-8
First find a common denominator of the expression ;
4/(x+8)(x-8) + 3 (x-8)(x+8)
Now whatever you multiplied on the bottom to find the common denominator , you must multiply to the numerator:
4(x-8)+3(x+8)
Now solve and simplfy:
4x-32+3x+24 =7x-8
Put this over your denominator :
7x-8/(x+8)(x-8) or 7x-8/x^2-64
Either of the above would be a valid answer
work citations ;
Regents exam questions , Algebra 2& trigonometry practice: addition and subtraction of rationals, pg 3, www.jmap.org
-When adding and subtracting rational expressions, it takes the same method as adding and subtracting fractions.
Example : 4/x+8 +3/x-8
First find a common denominator of the expression ;
4/(x+8)(x-8) + 3 (x-8)(x+8)
Now whatever you multiplied on the bottom to find the common denominator , you must multiply to the numerator:
4(x-8)+3(x+8)
Now solve and simplfy:
4x-32+3x+24 =7x-8
Put this over your denominator :
7x-8/(x+8)(x-8) or 7x-8/x^2-64
Either of the above would be a valid answer
work citations ;
Regents exam questions , Algebra 2& trigonometry practice: addition and subtraction of rationals, pg 3, www.jmap.org
1/2/13; How do we add and subtract rational expressions?
How do we add and subtract rational expressions?
Adding and subtracting rational expressionals are much like cross multiplying or adding and subtracting fractions , for example ;
First find the common denominator : 1/x + x/2y
the common denominator would be :2xy
Next, after finding the common denominators remember that whatever you multiply to the bottom you multiply to the top as well : 2y/2xy +x^2 /2xy
Now combine the expression : 2y +x^2 /2xy and that would be your final result
Adding and subtracting rational expressionals are much like cross multiplying or adding and subtracting fractions , for example ;
First find the common denominator : 1/x + x/2y
the common denominator would be :2xy
Next, after finding the common denominators remember that whatever you multiply to the bottom you multiply to the top as well : 2y/2xy +x^2 /2xy
Now combine the expression : 2y +x^2 /2xy and that would be your final result
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