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 September 13th, 2012, 02:15 PM #1 Newbie   Joined: Aug 2012 Posts: 16 Thanks: 0 rational expression Consider the rational expression a) Identify, if possible, a rational expression with integer coefficients that simplify to 2x+1/x-4, for each set of restrictions. i) x =/= -1,4 ii) x =/= 0,4 iii) x =/= 2/3, 4 iv) x=/= -1/2, 4 b) is there a rational expression with denominator of the form ax^2 +bx+c, a=/= 0, that simplifies to 2x+1/x-4, and has only the restriction x=/= 4? Explain
 September 13th, 2012, 09:07 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: rational expression a.) We are asked to consider: $\frac{2x+1}{x-4}$ We see that we must have $x\ne4$ Now, to add the restriction $x\ne k$ where $k\in\mathbb{R}$, yet have the expression simplify to the original, we must then multiply the original by 1 in the form of: $\frac{x-k}{x-k}$ Now, if k is a rational number, i.e., $k=\frac{a}{b}$ then we may write: $\frac{x-\frac{a}{b}}{x-\frac{a}{b}}=\frac{bx-a}{bx-a}$ Can you proceed to answer the four parts of the first problem now? Don't hesitate to ask for further assistance if you are still stuck! b.) Hint: Consider the denominator having the repeated root $x=4$...what does such a quadratic look like? What do you have to multiply the original denominator with to get this quadratic...and remember you must also multiply the original numerator by this factor. Let us know what you think.

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