How do you simplify
[2/(x+4)]+2
-----------
[3/(x+4)]+1
I know the answer is 2(x+5)/(x+7), but I have little idea how to get there! Please help?!
multiply your fraction by (x+4)/(x+4)
you end up with [2 + 2(x+4)]/[3 + (x+4)]
simplify and you will get your answer.
oooooooh thanks!
You're welcome! I'm glad I could help. Let me break down the process for you step by step.
To simplify the given expression:
1. Start by multiplying both the numerator and denominator of the first fraction, [2/(x+4)], by (x+4). This will eliminate the denominator and simplify the expression.
[2/(x+4)] * (x+4) = [2(x+4)]/(x+4) = 2
So, the numerator becomes 2.
2. Similarly, multiply both the numerator and denominator of the second fraction, [3/(x+4)], by (x+4).
[3/(x+4)] * (x+4) = [3(x+4)]/(x+4) = 3
So, the numerator becomes 3.
Now, the expression becomes:
[2 + 2(x+4)] / [3 + (x+4)]
3. Distribute the 2 inside the parentheses to simplify the numerator.
2 + 2(x+4) = 2 + 2x + 8 = 2x + 10
So, the numerator simplifies to 2x + 10.
4. Simplify the denominator by combining like terms.
3 + (x+4) = 3 + x + 4 = x + 7
So, the denominator simplifies to x + 7.
Putting it all together, the simplified expression is:
(2x + 10) / (x + 7)
Further simplifying the numerator, you can factor out a common factor of 2:
2(x + 5) / (x + 7)
Therefore, the final simplified expression is:
2(x + 5) / (x + 7)
I hope this explanation clarifies the process for you! Let me know if there's anything else I can assist you with.