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Simplify Complex Rational Expression

PaperStSoap

New member
Jun 26, 2012
9
(3/x-2) - (4/x+2) / (7/x2-4)

I got it down to...

-x+14/7

but the book is showing

x-14/7
 

Fantini

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
Welcome to MHB, Paper! :D

Which of these expressions did you mean:

$$\frac{3}{x-2} - \frac{ \frac{4}{x+2} }{ \frac{7}{x^2 -4} } \quad \text{ or } \quad \frac{ \frac{3}{x-2} - \frac{4}{x+2} }{ \frac{7}{x^2 -4} }?$$
 

soroban

Well-known member
Feb 2, 2012
409
Hello, PaperStSoap!

[tex]\dfrac{\dfrac{3}{x-2} - \dfrac{4}{x+2}}{\dfrac{7}{x^2-4}}[/tex]

I got it down to: .$\dfrac{-x+14}{7}$ . You are right!

But the book is showing: .$\dfrac{x-14}{7}$ . The book is wrong!
 

PaperStSoap

New member
Jun 26, 2012
9
Welcome to MHB, Paper! :D

Which of these expressions did you mean:

$$\frac{3}{x-2} - \frac{ \frac{4}{x+2} }{ \frac{7}{x^2 -4} } \quad \text{ or } \quad \frac{ \frac{3}{x-2} - \frac{4}{x+2} }{ \frac{7}{x^2 -4} }?$$
My apologies, the problem was the second one.
 

SuperSonic4

Well-known member
MHB Math Helper
Mar 1, 2012
249
My apologies, the problem was the second one.
You are right and the book is wrong. It's worth mentioning though that there is a restriction on the domain: $|x| \neq 2$.

(working in spoiler)


$\dfrac{\frac{3}{x-2} - \frac{4}{x+2}}{\frac{7}{x^2-4}}$

$\left(\frac{3}{x-2} - \frac{4}{x+2}\right) \cdot \frac{(x-2)(x+2)}{7}$

$\left(\frac{3(x+2)-4(x-2)}{(x-2)(x+2)}\right) \cdot \frac{(x-2)(x+2)}{7}$

$\frac{3x+6-4x+8}{7}$

$\frac{-x+14}{7}$