# Algebraic fractions

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• Sep 24th 2012, 12:15 PM
Ashir
Algebraic fractions

x^2 - 25/25 + 5x

I can factorize the numerator but not the denominator
I'm familiar with factorizing, canceling and expanding but I've never confronted something like 5x + 25 to expand/factorize.
• Sep 24th 2012, 12:21 PM
Ashir
Re: Algebraic fractions
(2.5 x 10^9)/(5 x 10^3)

in standard form. this isn't algebra but I'm hoping anybody has the patience to answer both.

Write as a single fraction in it's simplest form:

2x/x-1 - 7x-3/x^2-1

Please explain how you got these answers too, in the most efficient method.

Thanks!
• Sep 24th 2012, 12:26 PM
Siron
Re: Algebraic fractions
Quote:

Originally Posted by Ashir

x^2 - 25/25 + 5x

I can factorize the numerator but not the denominator
I'm familiar with factorizing, canceling and expanding but I've never confronted something like 5x + 25 to expand/factorize.

$\displaystyle 5x+25$, these two terms have a common factor $\displaystyle 5$ thus $\displaystyle 5x+25 = 5(x+5)$
• Sep 24th 2012, 07:11 PM
Wilmer
Re: Algebraic fractions
Quote:

Originally Posted by Ashir
(2.5 x 10^9)/(5 x 10^3)

2.5 * 10^9 / (5 * 10^3)
= 2.5 * 10^9 * 10^-3 / 5
= 5/2 * 10^6 / 5
= 5 * 10^6 / 10
= 5 * 10^5

Hope we're not doing your homework!!
• Sep 24th 2012, 07:21 PM
Prove It
Re: Algebraic fractions
Quote:

Originally Posted by Ashir

x^2 - 25/25 + 5x

I can factorize the numerator but not the denominator
I'm familiar with factorizing, canceling and expanding but I've never confronted something like 5x + 25 to expand/factorize.

Please use brackets where they're needed, or else learn some LaTeX. As written, your expression is \displaystyle \displaystyle \begin{align*} x^2 - \frac{25}{25} + 5x \end{align*}...
• Sep 24th 2012, 07:22 PM
MarkFL
Re: Algebraic fractions
Quote:

Originally Posted by Ashir
...

Write as a single fraction in it's simplest form:

2x/x-1 - 7x-3/x^2-1

I am assuming you mean:

$\displaystyle \frac{2x}{x-1}-\frac{7x-3}{x^2-1}$

First, factor the denominators:

$\displaystyle \frac{2x}{x-1}-\frac{7x-3}{(x+1)(x-1)}$

Now it is clear what we need to multiply the numerator and denominator of the first term with to get a common denominator:

$\displaystyle \frac{2x}{x-1}\cdot\frac{x+1}{x+1}-\frac{7x-3}{(x+1)(x-1)}$

Can you finish?
• Sep 25th 2012, 04:26 AM
Wilmer
Re: Algebraic fractions
Quote:

Originally Posted by MarkFL2
Can you finish?

No, I'm too busy. Could you finish it for me?
• Sep 25th 2012, 05:55 AM
MarkFL
Re: Algebraic fractions
Quote:

Originally Posted by Wilmer
No, I'm too busy. Could you finish it for me?

Ding! Fries are done.
• Sep 25th 2012, 08:06 AM
Ashir
Re: Algebraic fractions
Quote:

Originally Posted by Siron
$\displaystyle 5x+25$, these two terms have a common factor $\displaystyle 5$ thus $\displaystyle 5x+25 = 5(x+5)$

How could I not have saw that? Thanks.

Quote:

Originally Posted by Wilmer
2.5 * 10^9 / (5 * 10^3)
= 2.5 * 10^9 * 10^-3 / 5
= 5/2 * 10^6 / 5
= 5 * 10^6 / 10
= 5 * 10^5

Hope we're not doing your homework!!

Not following you. This area is very new to me, in fact we just started this week.

Nope, you're correcting the questions I didn't get right in an exam :0)

Quote:

Originally Posted by MarkFL2
I am assuming you mean:

$\displaystyle \frac{2x}{x-1}-\frac{7x-3}{x^2-1}$

First, factor the denominators:

$\displaystyle \frac{2x}{x-1}-\frac{7x-3}{(x+1)(x-1)}$

Now it is clear what we need to multiply the numerator and denominator of the first term with to get a common denominator:

$\displaystyle \frac{2x}{x-1}\cdot\frac{x+1}{x+1}-\frac{7x-3}{(x+1)(x-1)}$

Can you finish?

2X x X+1 = 2X+2 right? Or does the constant multiplied with the coefficient of the first term only apply to brackets?

And otherwise I'm lost on what I do next. We're revisiting this area after a year or so.
• Sep 25th 2012, 09:05 AM
Wilmer
Re: Algebraic fractions
Quote:

Originally Posted by Ashir
2X x X+1 = 2X+2 right?

Please use * for multiplication sign; and small "x" for variable...; and brackets when necessary...

2x * (x + 1) = 2x^2 + 2x ; everything inside brackets is multiplied by what's outside...
• Sep 25th 2012, 09:21 AM
Ashir
Re: Algebraic fractions
Forgot to times 2x by x sorry. Lost a good few marks on the exam because of clumsy mistakes
• Sep 25th 2012, 11:49 AM
Wilmer
Re: Algebraic fractions
Quote:

Originally Posted by Ashir
Forgot to times....

to MULTIPLY....
• Sep 25th 2012, 11:54 AM
Ashir
Re: Algebraic fractions
We say times here in England :P
• Sep 26th 2012, 12:06 PM
skeeter
Re: Algebraic fractions
Quote:

Originally Posted by cobooboc
I do not know why I proposed to be deleted, but I really do not understand that, can anyone give me an explanation?Or we do not have a common language.