Rational expressions with unlike denominators

[Desan65]

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.........

 

[tkhunny]

This?
\(\displaystyle \frac{1}{2x^{2}}+\frac{6x+3}{x^{2}}\)

Please use parentheses to clarify meaning.

 

[soroban]

Hello, Desan65!

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

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

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

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


\(\displaystyle \displaystyle\frac{1}{2x(x+3)}\cdot\frac{x}{x} \;+\;\frac{3}{x^2}\cdot\dfrac{2(x+3)}{2(x+3)} \;=\;\frac{x}{2x^2(x+3)} \:+\:\frac{6(x+3)}{2x^2(x+3)}\)

. . \(\displaystyle \displaystyle=\;\frac{x + 6(x+3)}{2x^2(x+3)} \;=\; \frac{x+6x+18}{2x^2(x+3)} \;=\;\frac{7x+18}{2x^2(x+3)} \)

 

[HallsofIvy]

Both Soroban and TKHunny interpreted what you wrote as (1 divided by 2x(sqr)) + ((6x + 3) divided by x(sqr) ).
\(\displaystyle \frac{1}{2x^2}+ \frac{6x+3}{x^3}\)

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

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

As TKHunny said, use parentheses!

 

[mmm4444bot]

I though the LCD was 2x(sqr) + 6

How did you decide that? Next time, please show what you've tried or explain what you're considering; this helps cut down on confusion. Cheers :cool:

 

[mmm4444bot]

Two other perfectly valid interpretations

The OP's ambiguous expression can be interpreted differently, yes, but the given answer tells us what the OP must have meant.

 

[robert mclaughlin]

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?

 

[JeffM]

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.

 

[harpazo]

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?