78 thousands = 7,800 ones. True or false
2 answers:
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Answer:
Step-by-step explanation:
We need to factor out numerator and denominator in order to simplify the rational expression by cancelling common factors.
Numerator : x^3 - 4 x = x (x^2 - 4) = x (x - 2) (x + 2)
Denominator (factoring by grouping):
x^2 - 5 x + 6 = x^2 - 3 x - 2 x + 6 = x (x - 3) - 2 (x - 3) = (x - 3) (x - 2)
Then we can cancel out the common factor (x - 2) in both numerator and denominator, leading to:
x (x + 2) / (x - 3) = (x^2 + 2)/ (x-3)
It depends on what you mean by the delimiting carats "^"...
Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for
.
In that case, you want to find the antiderivative,
Complete the square in the denominator:
Now substitute
, so that 
. Then
which simplifies to
Now, recall that
. But we want the substitution we made to be reversible, so that
which implies that
. (This is the range of the inverse sine function.)
Under these conditions, we have
, which lets us reduce 
. Finally,
and back-substituting to get this in terms of
yields
Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for
In that case, you want to find the antiderivative,
Complete the square in the denominator:
Now substitute
which simplifies to
Now, recall that
which implies that
Under these conditions, we have
and back-substituting to get this in terms of