- 2x^3
2x√(x^2+5) -----------
x^2+5
--------------------------------------- ***The lines are fraction lines***
x^2+5
This question asks you to simplify or perform the indicated operation. The answer is also given as 10x
----------
(x^2+5)^3
can someone help explain how they got the answer?
oops it didnt work correctly
2x√(x^2+5) -2x^3/x^2+5
---------------------------------
x^2+5
The answer was
10x
--------------
(x^2+5)^3
2x√(x^2+5) -2x^3/(x^2+5)
--------------------------------- ?????
(x^2+5)
================================
2x (x^2+5)^(3/2) - 2 x^3
---------------------------------
(x^2+5)^2
===================================
2x(x^2+5)^(5/2) -2 x^3 (x^2+5)
-----------------------------------------
(x^2+5)^3
=================================
2x[ (x^2+5)^(5/2) -x (x^2+5) ]
---------------------------------------
(x^2+5)^3
============================
2x[ (x^2+5)^(5/2) -x (x^2+5) ]
---------------------------------------
(x^2+5)^3
how you get the numerator to be 2x * 5 I do not know
well one error: note -x^2 not -x
============================
2x[ (x^2+5)^(5/2) -x^2 (x^2+5) ]
---------------------------------------
(x^2+5)^3
To simplify the given expression:
1. Start by simplifying the numerator and denominator separately:
In the numerator, we have 2x√(x^2+5). Since the square root (√) cannot be simplified further, we leave it as it is.
In the denominator, we have x^2 + 5, which doesn't have any simplification either.
2. Combine the numerator and denominator to form the fraction:
The simplified numerator is 2x√(x^2+5), and the simplified denominator is (x^2 + 5)(x^2 + 5), or (x^2 + 5)^2.
So the fraction becomes:
2x√(x^2+5)
---------------
(x^2+5)^2
3. To simplify further, we can multiply the numerator and denominator by the conjugate of the numerator, which is the same expression but with the opposite sign for the radical term. This will help us eliminate the square root in the numerator:
Multiplying the numerator and denominator by 2x√(x^2+5):
(2x√(x^2+5)) * (2x√(x^2+5))
-------------------------
(x^2+5)^2
This simplifies to:
(4x^2(x^2 + 5))
-------------
(x^2+5)^2
4. Now we can simplify further by cancelling out common factors:
The (x^2 + 5) in the numerator and the denominator can be cancelled out, leaving:
4x^2
------
(x^2+5)
5. Finally, we have the simplified expression:
4x^2
------
(x^2+5)
Note: The answer you provided (10x / (x^2+5)^3) doesn't match the simplified expression. Double-check the given answer.