x+y = 47
x-y = 21
------------ add together
2x =68 divide by 2
x=34
x+y = 47
34+ y = 47
subtract 34 from each side
y = 13
the two numbers are 34 and 13
Hello!

The fraction 18/24, reduced to its lowest terms, is:

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Divide both the numerator and the denominator by the GCD of 18 and 24, which is 6:
18 ÷ 6 = 3
24 ÷ 6 = 4
It's simplest form would be 3/4. This cannot be reduced further.
Yes, you're right! The first step is rewriting the equation as

Subtract
from both sides:

Use the property
to rewrite the equation as

Divide both sides by 

Alternative strategy:
Consider both sides as exponents of e:

Use
to write

Divide both sides by a:

Consider the logarithm base b of both sides:

The two numbers are the same: you can check it using the rule for changing the base of logarithms
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Depending on the value of 't' and 'u', the numerical value of that expression
could have almost anything for factors.
For example, if 't' happens to be 3 and 'u' happens to be 10, then 6tu = 180,
and the factors of 6tu are
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
But that would only be temporary ... only as long as t=3 and u=10.
The only factors you can always count on, that don't depend on the values
of 't' and 'u', are
1, 6, t, u, 6t, 6u, tu, and 6tu .
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