Add. Simplify, if possible.
4d/(5d-10) + 2d/(10d-20)
I am simply having a difficult time with this one. Could you please just get me started?
Thank you in advance!
Ok, I gave it one more shot. PLEASE let me know if the answer is correct?
10d/[10(d-2)]
Or, should I leave it as 10d/(10d-20), or do I factor out both of the 10d's to come up with -1/20?
Please help me?
10d / 10(d - 2) = d / (d - 2)
You were very close!
Of course! To simplify the expression, we need to combine the terms with the same variable, if it's possible.
Let's start by finding the least common multiple (LCM) of the denominators (5d-10) and (10d-20). The LCM is the smallest multiple that both denominators have in common.
To find the LCM, we need to factorize the denominators first.
For (5d-10):
The expression can be factored as 5(d-2).
For (10d-20):
First, factor out 10: 10(d-2).
Now, we have a common factor of (d-2) in both denominators. Therefore, the LCM is 5(d-2).
Next, we'll rewrite the fractions with the common denominator, 5(d-2).
For the first term, 4d/(5d-10), we need to multiply the numerator and denominator by (d-2) to have a common denominator:
4d ⋅ (d-2) / (5d-10) ⋅ (d-2)
Simplifying the numerator, we get 4d² - 8d.
Applying the same steps to the second term, 2d/(10d-20):
2d ⋅ (d-2) / (10d-20) ⋅ (d-2)
The numerator simplifies to 2d² - 4d.
Now, our expression becomes:
(4d² - 8d) / (5d-10) + (2d² - 4d) / (10d-20)
We have successfully simplified the expression by finding a common denominator. However, the expression can be further simplified by simplifying the terms in the numerator, if possible.