Algebraic Fraction: How to Solve and Simplify?

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Discussion Overview

The discussion revolves around solving and simplifying an algebraic fraction equation involving the expression $$\frac{3 }{ 2(x+1)} + \frac{1}{x+1} = \frac{5}{6}$$. Participants seek assistance in understanding the steps to solve this equation, including finding a common denominator.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant requests help with the equation and asks for detailed explanations of the steps involved.
  • Another participant suggests considering the common denominator for the fractions involved, hinting at the need to find a common denominator.
  • Some participants express uncertainty about what the common denominator should be, proposing different possibilities such as (x+1) or 2.
  • A later reply clarifies that the common denominator should include factors of (x + 1) and 6, concluding that it is 6(x + 1).
  • One participant suggests multiplying the numerator and denominator of the second term to equate it with the first term, leading to a simplified equation and a proposed solution for x.
  • Verification of the solution by substituting the value of x back into the original equation is mentioned.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the common denominator and propose different approaches, indicating that there is no consensus on the best method to solve the equation.

Contextual Notes

Some steps in the mathematical reasoning remain unresolved, particularly regarding the verification process and the implications of the proposed common denominators.

mathlearn
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Hi,


$$\frac{3 }{ 2(x+1)} + \frac{1}{x+1} = \frac{5}{6}$$
Can you help me on this problem. I'm not sure on how to solve this and please be kind enough to explain your steps little bitMany Thanks:)
 
Last edited:
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mathlearn said:
Hi,


$$\frac{3 }{ 2(x+1)} + \frac{1}{x+1} = \frac{5}{6}$$
Can you help me on this problem. I'm not sure on how to solve this and please be kind enough to explain your steps little bitMany Thanks:)
Hint: What is the common denominator for these fractions?

-Dan
 
Last edited by a moderator:
not sure might be (x+1) or 2,1?? :)
 
mathlearn said:
not sure might be (x+1) or 2,1?? :)
The common denominator will contain 3 terms: (x + 1), 2(x + 1), and 6. So it must have one factor of (x + 1) and a factor of 6. (The 6 = 2 x 3, so it contains the 2 automatically.) So you are looking for 6 (x + 1), right? Can you take it from there?

-Dan
 
Just multiply the numerator and denominator of second term of LHS by 2 to equate it's denominator to the first term of LHS.

$$\frac{3}{2(x+1)} + \frac{1}{x+1} = \frac{5}{6}$$

$$\frac{3}{2(x+1)} + \frac{{\color{red}{2}} \cdot 1}{{\color{red}{2}} \cdot (x+1)} = \frac{5}{6}$$

$$\frac{5}{2(x+1)} = \frac{5}{6}$$

$$x=2$$

Verify it by substituting the value of $x$ to be 2 in the LHS.
 
Many Thanks (Smile)
 

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