Expressions with (6/x+2) + (8/x+3)

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In summary, the simplified form of the expression (6/x+2) + (8/x+3) is (14x + 38) / (x + 5). It cannot be simplified further. The domain of the expression is all real numbers except for x = -2 and x = -3 due to division by zero. It is not defined for these values. This expression can be used in real-world applications for calculating totals, averages, and representing relationships between two variables in mathematical models.
  • #1
ValiantKhan
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If i have something like (6/x+2) + (8/x+3) how to i do that?

aren't i supposed to invert and multiply or something, thanks

--Val
 
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  • #2
[tex]\frac{6(x+3)}{(x+2)(x+3)} + \frac{8(x+2)}{(x+2)(x+3)}[/tex]

You just need to find a common denominator.
 
  • #3
ValiantKhan said:
aren't i supposed to invert and multiply or something, thanks

That's for division by a fraction, in which case you multiply by the reciprocal.
 
  • #4
Since the two denominators are x+2 and x+3 the common denominator will be (x+2)(x+3).

It's just like 1/2+ 1/3= (1/2)(3/3)+ (1/3)(2/2)= 3/6+ 2/6= 5/6.
 

Related to Expressions with (6/x+2) + (8/x+3)

1. What is the simplified form of the expression (6/x+2) + (8/x+3)?

The simplified form of this expression is (14x + 38) / (x + 5).

2. Can the expression (6/x+2) + (8/x+3) be simplified further?

No, the expression has already been simplified as much as possible.

3. What is the domain of the expression (6/x+2) + (8/x+3)?

The domain of this expression is all real numbers except for x = -2 and x = -3, since these values would result in a division by zero.

4. Is the expression (6/x+2) + (8/x+3) defined for all values of x?

No, the expression is not defined for x = -2 and x = -3 due to division by zero.

5. How can this expression be used in real-world applications?

This expression can be used in various situations where quantities are being combined or added together, such as calculating the total cost of items with different prices or finding the average of two values with different weights. It can also be used in mathematical models to represent relationships between two variables.

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