Math expression needs to be solved.

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Math expression needs to be solved.

3/(2x+4) + 2/(3x+6)

Posted 195 day ago

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Answers (17)

asad.taj

3*(3x+6)+2*(2x+4)
= 9x+18+4x+8
=13x+26
=13(x+2)

Posted 193 day ago

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I have solved this problem, but there is a problem in the format of writing.
So, I will answer again.

Take the lcm of the denominators, which is

6( x+2)^2

therefore, the given expressions will be simplyfy as follows:

3/(2x+4) + 2/(3x+6)
= 3(3x+6) + 2(2x+4) / 6(x+2)^2
= 9x+18+4x+8 / 6(x+2)^2
= 13x + 26 / 6(x+2)^2
= 13(x+2) / 6 (x+2)^2

= 13
------------- this is the answer.
6( x + 2 )

Posted 194 day ago

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First, I want to tell all math teachers that the you can only, find the new expression, but you can not find the any value of given variable x. To find the value of any variable you have to have an equation. You can only just simplyfied.

This the additon operation of two expressions.

We are given, 3/(2x+4) + 2/(3x+6)
First, take LCM of the denominators.

LCM = (2x+4)(3x+6) = 6(x+2)^2
now, simplyfy the given expression.

3(3x+6) + 2(2x+4) 9x +18 +4x + 8
= ----------------------- = -------------------
6 ( x + 2 ) ^2 6 ( x + 2 )^2

= 13x + 26 13 ( x + 2 ) 13 1
------------ = ----------------- = ----- . -------- This is the answer
6 ( x + 2 ) ^2 6 ( x + 2 ) ^2 6 ( x + 2 )

Posted 194 day ago

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atta

f(x) = 3/(2x + 4) + 2 / (3x + 6) => f(x) = R(x) = N(x) / D(x) entails rules of fractions such as
a/b + c/d = ad +bc / bd thus yielding 3/(2x + 4) + 2 / (3x + 6) => 3(3x + 6) + 2(2x +4) / (2x + 4)(3x + 6) = 9x + 18 + 4x + 8 / (2x + 4)(3x + 6) = 13x + 26 / (2x + 4)(3x + 6) = 13x + 26 / 6x^2 + 24x + 24. To solve the rational expression, you muset set the numerator N(x) = 0 as in 13x + 26 = 0 yielding x = -26/13.

J.C

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jayteacher

Correct me if I am wrong, someone, but I believe that what rajbaba78 said: (the expression) "cannot be solved for x!" is correct. The word solved implies that there is a solution to an equation, I believe. However, a mathematical expression can only be simplified, reduced to lowest terms, or evaluated (for x in the above expression, if x = any real or complex number).

Posted 195 day ago

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marycurry

Use distributive property: 3(2x) + 3(4) + 2(3x) + 2(6) = 6x + 12 + 6x + 12 = 12x +24. If need be, this can be divided by 12 giving you x + 2.

Posted 195 day ago

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We can only simplify the given expression. It cannot be solved for x!

3/(2x+4)+2/(3x+6) =
3/2(x+2) + 2/3(x+2) =
9/6(x+2) + 4/6(x+2) =
13/[6(x+2)]<===simplified answer.

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YummyCookies

13 / [6(x + 2)]

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math_fanatic

I was incorrect when I said the two denominators have no factors in common.
As the poster just before me mentioned, the process would be shorter if you noticed
that the two denominators had a common factor of (x + 2) however if you DON'T notice it,
like I didn't, don't worry. You'll still come up with the same answer simply by multiplying the
two denominators together. :D

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math_fanatic

The first step in simplifying this expression is to find a common denominator:

Since the two denominators have no factors in common, the common denominator
is the two denominators multiplied together: (2x + 4)(3x + 6)

multiply the first term by (3x + 6)/(3x + 6) which is the same as multiplying by one:
3(3x + 6)/[(2x + 4)(3x + 6)]

next multiply the second term by (2x + 4)/ (2x + 4):
2(2x + 4)/[(3x + 6)(2x + 4)]

Now we have two terms with the same denominator so we can now add the numerators:
3(3x + 6) + 2(2x + 4) = 9x + 18 + 4x + 8 = 13x + 26 <------NEW NUMERATOR!

now we have (13x + 26)/[(3x + 6)(2x + 4)]

Factor out a 13 out of the the numerator:
13(x + 2)/ [(3x + 6) (2x + 4)

We'd like to have an x + 2 on the bottom so we can cancel out the one on the top so factor out the 3 from the (3x + 6) and the 2 from the (2x + 4):
13(x + 2)/[3(x + 2) * 2(x + 2)]

Simplifying we get:
13(x + 2)/[6(x + 2)^2]

Now we can cancel the x + 2 on the top with one of the x + 2 's on the bottom and we're left with:
13/[6(x + 2)] = 13/(6x + 12)

13/(6x + 12) is the final answer.

Posted 195 day ago

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jayteacher

A simplier way to find the solution is to notice the 2x + 4 and 3x + 6 both have a common factor x + 2. Therefore, the expression can be written as: [3 / 2(x + 2)] + [2 / 3(x + 2)].
When the two numerators and demoninators are multiplied by the same factor (3 and 2, respectively), the two numerators are 3*3 and 2*2, and the lowest common denominator is now 2*3*(x+2).
This expression now looks like: [3*3 / 3*2(x+2)] + [2*2 / 2*3(x+2)]
The numerator now becomes 3*3 + 2*2 = 13.
The simplified answer: 13 / [6(x + 2)]

Posted 195 day ago

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jayteacher

This problem requires lots of division bars, so I hope that the reader will rewrite the problem as a math textbook would. Unfortunately, tutor answers does not give us an array of different ways to write a problem. Oh, well. The solution process to the expression is as follows.

1. Find the lowest common denominator, which is (2x+4)(3x+6).
2. Since 2x+4 is already in the 1st division, and since 3x+6 is already in the 2nd division, the numerator and denominator of the 1st division must be multiplied by 3x+6, and the numerator and denominator of the 2nd division must be multiplied by 2x+4.
3. It looks like: [3(3x+6)] / [(2x+4)(3x+6)] + [2(2x+4)] / [(2x+4)(3x+6)]
4, Since the expression now has common denominators, the denominators can be combined, and the numerators can be combined. The next steps would be to use the distributive property in the numerator: 3(3x+6) = 9x + 18 and 2(2x+4) = 4x + 8, and then add like terms: 9x + 4x = 13x and 18 + 8 = 26.
5. The above steps derive an expression that looks like: [13x+26] / [(2x+4)(3x+6)].
6. Now, factor terms from the numerator and the denominator: [13(x+2)] / [2(x+2) * 3(x+2)].
7. After dividing the numerator and the denominator by x+2, the simplified answer is 13 / [6(x+2)].

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sufudge

6x + 12 + 6x +12
6x + 6x +12 +12
12x +12

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MFB13

Here is how I go about simplifing this expression:

3/(2x+4) + 2(3x+6) = [ 3(3x+6) + 2(2x+4)] / [(2x+4)(3x+6)] = (9x + 18 + 4x + 8)/ [(2x+4)(3x+6)] =

(13x + 26)/[2(x+2)3(x+2)] = 13(x + 2) / [6(x+2)(x+2)] = 13 / [6(x+2)] final simplified expression

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Doctor Bob

This is a perfect example of how the division sign in a fraction is a GROUPING symbol, keeping its expressions together.
You have two different denominators 2x + 4 and 3x + 6 which means you need a COMMON denominator. You get a common denominator in the same way you would get one if you added 1/6 + 1/4.
(6 x 4 = 24 , i.e., the 24 is common to both 6 and 4. It is more complicated in Algebra but the same principle).
My common denominator is (2x+4)(3x+6).
I now divide each OLD denominator into the NEW COMMON DENOMINATOR and then multiply by the numerator.
And so my new fraction is

3(3x+6) + 2(2x+4)
-------------------------
(2x+4) (3x+6)

Earlier I canceled out the terms in the numerator and denominator but one cannot do that due to the central PLUS sign in the numerator. If the parenthetical terms in the numerator were related by multiplication, I could cancel. I fell for the old PLUS SIGN trick. RevDrBob@aol.com with egg on his face.

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Doctor Bob

OOPS- I made the classic mistake of canceling out terms when they are separated by a PLUS sign. One can only do that if it is MULTIPLICATION. And so, this answer is wrong. I need to re-do,

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Doctor Bob

This is a perfect example of how the division sign in a fraction is a GROUPING symbol, keeping its expressions together.
You have two different denominators 2x + 4 and 3x + 6 which means you need a COMMON denominator. You get a common denominator in the same way you would get one if you added 1/6 + 1/4.
(6 x 4 = 24 , i.e., the 24 is common to both 6 and 4. It is more complicated in Algebra but the same principle.
My common denominator is (2x+4)(3x+6).
I now divide each OLD denominator into the NEW COMMON DENOMINATOR and then multiply by the numerator.
And so my new fraction is

3(3x+6) + 2(2x+4)
-------------------------
(2x+4) (3x+6)

Note how I can cancel out ALL of the parentheses in both numerator and denominator.
I am left with 3+2 = 5

Ask if you need more explanation. RevDrBob@aol.com

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