Question

help

Answer 1

\[\frac{ \frac{ 1 }{ x } -\frac{ 1 }{ 5 }}{ \frac{ 1 }{ x^2 } -\frac{ 1 }{ 25}}\]

Answer 2

I got x/-x = -1

Answer 3

and what is

Answer 4

25x^2

Answer 5

There are 2 fractions in the numerator and 2 fractions in the denominator.
The denominators of the 4 fractions are x, 5, x^2, and 25.
What is the LCD of all 4 denominators?

Answer 6

Great.
Let's multiply the numerator and denominator of the main fraction by the LCD of all the small fractions to eliminate the small fractions.

Answer 7

I got -1 as my fina result

Answer 8

\(\Large = \dfrac{ 25x^2(\frac{ 1 }{ x } -\frac{ 1 }{ 5 })}{ 25x^2(\frac{ 1 }{ x^2 } -\frac{ 1 }{ 25})}\)

Answer 9

\(\Large = \dfrac{ 25x - 5x^2}{25 - x^2}\)

\(\Large = \dfrac{ 5x(\cancel{5 - x})}{(5 + x )(\cancel{5 - x})}\)

Answer 10

\(\Large = \dfrac{ 5x}{5 + x}\)

Answer 11

That's what I get

Answer 12

I simplified the num and den seperatley, than divided the den by num.

Answer 13

$$ x \ne \pm5$$ :-)

Answer 14

Other approach:

\(\Large \dfrac{ \frac{ 1 }{ x } -\frac{ 1 }{ 5 }}{ \frac{ 1 }{ x^2 } -\frac{ 1 }{ 25}}=\)

\(\Large =\dfrac{ \frac{ 1 }{ x } -\frac{ 1 }{ 5 }}{ (\frac{ 1 }{ x } -\frac{ 1 }{ 5})( \frac{ 1 }{ x } +\frac{ 1 }{ 5} )}\)

\(\Large =\dfrac{ \cancel{\frac{ 1 }{ x } -\frac{ 1 }{ 5 }}~~1}{ \cancel{(\frac{ 1 }{ x } -\frac{ 1 }{ 5})}( \frac{ 1 }{ x } +\frac{ 1 }{ 5} )}\)

\(\Large =\dfrac{ 5x \times 1}{ 5x \times ( \frac{ 1 }{ x } +\frac{ 1 }{ 5} )}\)

\(\Large =\dfrac{ 5x}{ 5 + x}\) ; \(x \ne \pm 5\)

Answer 15

ehy do you have to put the 5x on the last step? Why not