Rational Definition and 616 Threads

Suppose a, b, and c are integers and x, y, and z are nonzero real numbers that satisfy the following equations: xy/x+y = a xz/x+z = b yz/y+z = c Is x rational? If so, express it as a ratio of two integers. I am pretty sure x is rational, but I don't know how to get the ratio. I am...

Hello! Are all rational expression of two linear expression, say f (x) = (x + 3)/(x - 3), bijective? How will x = 3 affect the condition of a bijective function?

I got a few questions. First of all, I reduced 3715/990 to 743/198. Is that reduced all the way? Second, using the natural number, 1-10, as either the numerator or denominator of a fraction, there is 100 fractions, 1/1, 2/1,...,10/1, 1/2, 2/2,...10/10. How many of these reduce to integers. I...

Is there an accurate way to write the value of an Irrational number? If there is no an accurate way to write the value of an Irrational number, then can we conclude that no irrational number has an exact place on the real line? And if there is an exact place to an irrational number on the...

Hi everyone, I need to prove that any number with a repeating block of digits is a rational number. Someone told me I should first find a method of constructing a rational number in the form a/b from a number with repeating blocks of digits (and to do it with very 'easy' numbers first). I'm...

"The rational choice is not always the one with the most humanity in it" Give me your point of view about this quotation. You may agree or disagree with it.

How can you tell the two apart? Here are some examples in the book: 1. 3x^3 + 2x + 1 2. 3x^2 + (x + 1)^1/2 3. \frac{2x + 3}{x^2 + 1} 4. (\frac{x}{x + 1})^X

If y>x where x and y are both elements of the reals, but x is also irrational, I must prove that there is a rational number z such that x<z<y. I can only show this is true when x is rational. How do you add something to an irrational number to make it rational?

Most of you have probably heard a phrase along the lines of "man the rational animal". I think that it is fairly obvious that this phrase is meant to refer to the the idea that man has rational abilities, not that he is impervious to irrational emotions. Perhaps it is supposed to suggest that...

How do I solve the integration of a rational function such as: x^2 - 6x - 2 (x^2 + 2)^2 If possible, please list the general rule of solving, I DO NOT want the answer, I simply want to know the way of solving it. Thanks in advance! So far I got to the part where A = 1, B = -6 and...

How do I solve the integration of a rational function such as: x^2 - 6x - 2 (x^2 + 2)^2 If possible, please list the general rule of solving, I DO NOT want the answer, I simply want to know the way of solving it. Thanks in advance!

Can someone pls help me solve this integral? integral of (6x^2-13x-43)dx/(x^3-1x^2-8x+12) it's supposed to be solved using partial fractions, but I am having trouble factoring the denom correctly so I can apply it... Thanks

can e to any real powers give you a rational number?

Does there exist a rational number ratio for any two irrational numbers?

I've just finished reading the section on partial fraction integration from my text. The book describes how all rational functions can be integrated by performing a partial fraction decomposition and subsequently integrating the partial fractions using methods that are already known. I tried to...

What generalizations can be made concerning fractals of nonzero rational dimensions M/N (where M and N are nonzero integers)? How does a fractal of non-integral dimension F compare geometrically to a fractal of dimension GF, where G is a nonzero integer?