Rational expressions with unlike denominators

Desan65

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Find 1 divided by 2x(sqr) + 6x + 3 divided by x(sqr)
I know that the answer is 7x +18 divided by 2x(sqr)(x + 3), but I don't know how they got it.
I though the LCD was 2x(sqr) + 6.........
 
This?
12x2+6x+3x2\displaystyle \frac{1}{2x^{2}}+\frac{6x+3}{x^{2}}

Please use parentheses to clarify meaning.
 
Hello, Desan65!

Find: 12x2+6x+3x2\displaystyle \text{Find: }\,\dfrac{1}{2x^2 + 6x} + \dfrac{3}{x^2}

Answer: 7x+182x2(x+3)\displaystyle \text{Answer: }\,\dfrac{7x +18}{2x^2(x + 3)}

We have: 12x(x+3)+3x2\displaystyle \text{We have: }\:\dfrac{1}{2x(x+3)} + \dfrac{3}{x^2}

The LCD is: 2x2(x+3)\displaystyle \text{The LCD is: }\,2x^2(x+3)


12x(x+3)xx  +  3x22(x+3)2(x+3)  =  x2x2(x+3)+6(x+3)2x2(x+3)\displaystyle \displaystyle\frac{1}{2x(x+3)}\cdot\frac{x}{x} \;+\;\frac{3}{x^2}\cdot\dfrac{2(x+3)}{2(x+3)} \;=\;\frac{x}{2x^2(x+3)} \:+\:\frac{6(x+3)}{2x^2(x+3)}

. . =  x+6(x+3)2x2(x+3)  =  x+6x+182x2(x+3)  =  7x+182x2(x+3)\displaystyle \displaystyle=\;\frac{x + 6(x+3)}{2x^2(x+3)} \;=\; \frac{x+6x+18}{2x^2(x+3)} \;=\;\frac{7x+18}{2x^2(x+3)}
 
Both Soroban and TKHunny interpreted what you wrote as (1 divided by 2x(sqr)) + ((6x + 3) divided by x(sqr) ).
12x2+6x+3x3\displaystyle \frac{1}{2x^2}+ \frac{6x+3}{x^3}

Two other perfectly valid interpretations are (1 divided by (2x(sqr)+6x))+ (3 divided by x(sqr)).
12x2+6x+3x\displaystyle \frac{1}{2x^2+ 6x}+ \frac{3}{x}

or (1 divided by 2x(sqr)+ 6x+ (3 divided by x(sqr))
12x+6x+3x2\displaystyle \frac{1}{2x}+ 6x+ \frac{3}{x^2}

As TKHunny said, use parentheses!
 
simplify rational expression

i cant figure out how to post a new question, so i hope someone sees this

1 x+3
____ - ________i get
x^2-9 x^2-2x-3



x^2-2x-27
________
x^2+27


(x-1)
= _______
(x+1)


i also get 1
___
(x+3) or x-3

which direction should i be heading?
 
Last edited:
i cant figure out how to post a new question, so i hope someone sees this

1 x+3
____ - ________ i get x^2-2x-3 - x^2-27
x^2-9 x^2-2x-3 ____________________

x^2+27


(x-1)
= _______
(x+1)


i also get 1
___
(x+3) or x-3

which direction should i be heading?
When you get to the page for your topic, you will see toward the upper left of the screen a button marked "post new thread."

It is much better to use parentheses and / to indicate division if you are trying to write fractions without special software.

As it is, I think you may be asking about an expression that starts [(x + 3) / (x^2 - 9)]. What happens beyond that is impossible for me to guess.
 
Adding Algebraic Fractions

Find 1 divided by 2x(sqr) + 6x + 3 divided by x(sqr)
I know that the answer is 7x +18 divided by 2x(sqr)(x + 3), but I don't know how they got it.
I though the LCD was 2x(sqr) + 6.........



1/(2x^2) + (6x + 3)/x^2

Desan65:

Is this the proper addition?
Is this what you were trying to type?
 
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