1. I

    Breaking apart a Denominator

    This is a step in a current calculus problem am I attempting. This rewriting is essential to being able to solve the integral, but I am unsure how the author went between these two steps. To my knowledge, denominators cannot be broken apart. He seems to have moved a u to the outside and taken...
  2. M

    Enter the exact answer as a single fraction. Rationalize the denominator, if required

    cos(cos-13/4+tan-13) Enter the exact answer as a single fraction. Rationalize the denominator, if required
  3. R

    Division - with Division in the Denominator

    Would anyone be so kind as to show me how to simplify (reduce) this equation? (Happy)
  4. D

    Rationalising a negative denominator in an inequality

    So, I have the inequality: 3x+4 > 5√3x +6 This works out to: x > (5√3 + 3)/-33 However... the textbook I am working from gives the answer (as a fraction) x < - (5√3 + 3)/33 Have I missed something when dividing by -1? I get that multiplying both sides of the equation by -1 flips the...
  5. T

    Least Common Denominator

    Hello! I was wondering if anyone could help me out with this. I'm not really sure where to start... I might just be blanking at the moment but it would be great if someone could walk me through it! The problem is asking for the you to find the equivalent fractions with the least common...
  6. R

    Rationalize Denominator and Numerator

    Why do math teachers stress the process of rationalizing numerator and denominator? This is more a problem, I see, in terms of rationalizing the denominator. Why can't fractions have a radical in the denominator? What's the big deal?
  7. S

    How to find the least common denominator

    Help me to find the lcd of 2/3, 5/12, 4/10
  8. S

    Integral with trig functions in the denominator

    To integrate this equation, the only thing I could think of to solve is to use u substitution, u =tan (theta)/2, then sine would be 2u/(u^2+1) and cosine (1-u^2)/(u^2+1). However following this process I run into a brick wall when I simplify the substitution into a fraction with a fourth degree...
  9. L

    Why Do You Divide Bottom Denominator of Limit by -X When it Approach -Infinity?

    Hi everyone! I was doing a homework assignment involving limits today, and something came up that didn't make any sense at all to me. In the example for finding the lim (x-> -Infinity) (3x-2)/sqrt(2x^2+1), the examples says to divide both the numerator and denominator by x. It does this in a...
  10. H

    finding derivataive with square roots in denominator

    Here's the question: Differentiate: f(t)=2t/(2 +sqrt t). I know I use the Quotient Rule. (f/g)'= (gf'-fg')/g^2. Numerator of function is f, denominaator is g. I think my difficulties lie in figuring the derivative of sqrt t. Plug in for f and g: (2 + sqrt t)(2t)'-(2t)(2+sqrt t). This is...
  11. A

    Finding the range, radical in the denominator

    Hi, I am trying to find the range of f(x) = 1 / [sqrt(x+3)] I know that the function is undefined when x+3 =< 0 so the domain is all x>-3 As the denominator must be positive, i know that f(x) > 0 and i believe that is the range. I am having trouble knowing how I should set this out on...
  12. A

    Help for $U = T^2$ has an $F$ distribution with 1 numerator and $v$ denominator degre

    If $T$ has a $t$ distribution with $v$ degrees of freedom, then $U = T^2$ has an $F$ distribution with 1 numerator and $v$ denominator degrees of freedom. First, I set $$T = \frac{Z}{\sqrt(W/v)}$$, where $T$ is t distribution with $v$ df, W is a chi-squared distributed variable with v df, and...
  13. nycmath

    Numerator Degree < Denominator Degree

    If the numerator degree is less than denominator degree, what is the oblique or slant asymptote? T(x) = (x^3)/(x^4-1)
  14. S

    Stuck on quotient of two polynomials

    Hello (x-a)(x-b) / (c-a)(c-b) + (x-a)(x-c) / (b-a)(b-c) = (x-a)(x-b)(b-a) - (x-a)(x-c)(c-a) / (c-a)(c-b)(b-a) My textbook suggests the absence of (b-c) in the denominator is accounted by the fact that b-c = -(c-b) . I understand this to imply that (c-b) and (b-c) cancel each other out. Yet...
  15. D

    Rationalizing denominator

    I just need to understand how rationalized \frac{2}{\sqrt{2\pi}} to get \sqrt{\frac{2}{\pi}} When I rationalized, I just multiplied by \frac{\sqrt{2\pi}}{\sqrt{2\pi}} and got \frac{\sqrt{2\pi}}{\pi}
  16. E

    Infinite Series with Numerator Arithmetic and Denominator Geometric

    (1/1) + (4/4) + (7/16) + (10/64) ... This series is supposed to be an infinite series but it's not going up by a set common ratio. How do I find the sum of the infinite series of this series?
  17. E

    identity proving with two terms in denominator

    I have a trig identity proving question: (1 - sin(x))/(1 + sin(x)) = tan(x) + 1/cos(x) by multiplying 1 - sin(x) on left side doesn't seems work. Anyone can help. Thanks in advanced.
  18. C

    Help me understand solving x in denominator (very basic)

    Hi I'm new to the boards and wondering if anyone can help me wrap my head around the steps it takes to solve this basic question, I believe I have it right but I just want to be sure I haven't just stumbled upon a pattern to solve this question. 1/x+2 = 5 So you could say 1 = 5(x+2) = 5x + 10...
  19. M

    Find a fraction between 97/36 and 96/35 with smallest denominator

    Find a fraction between 97/36 and 96/35 which has the smallest denominator. Since 97/36 > 96/35, I formed the following inequality \frac {97}{36} < \frac pq < \frac{96}{35} \, . Now, appropriately so, we could write the given fractions with common denominators and thusly yield \frac...
  20. H

    Rationalizing the denominator that is a cube root?

    I need help rationalizing the denominator if it is a cube root. I understand the if it is just a square root, you multiply it by itself. But im having trouble with rationalizing a cube root. Here is the problem i need help with: (3a)/(∛25a)