# newby needing to know how to combine a natural number and an algebraic fraction

• Nov 15th 2011, 02:09 PM
ahdavewest751
newby needing to know how to combine a natural number and an algebraic fraction
Im new to algebra and need to know how:

1 + 2/x^2 + 4 can be combined into 1 term

thanks
• Nov 15th 2011, 02:17 PM
e^(i*pi)
Re: newby needing to know how to combine a natural number and an algebraic fraction
Quote:

Originally Posted by ahdavewest751
Im new to algebra and need to know how:

1 + 2/x^2 + 4 can be combined into 1 term

thanks

Are you familiar with adding numerical fractions? If so you know that to add fractions we need to have a common denominator.

Spoiler:
For example $\displaystyle \dfrac{2}{3} + \dfrac{1}{7} = \dfrac{2}{3} \times \dfrac{7}{7} + \dfrac{1}{7} \times \dfrac{3}{3} = \dfrac{14}{21} + \dfrac{3}{21} = \dfrac{17}{21}$. For integers (whole numbers) you learned that you multiply top and bottom but whatever suited.

First you may as well say that $\displaystyle 1+4 = 5$ to make our life easier

It is the same principle with algebra, you want to get it so that $\displaystyle 5 \text{ and }\dfrac{2}{x^2}$ have the same denominator. So what would you multiply $\displaystyle \dfrac{5}{1}$ by to get a common denominator?
• Nov 15th 2011, 02:32 PM
ahdavewest751
Re: newby needing to know how to combine a natural number and an algebraic fraction
ok so I tried this:

1 + 2/x^2 + 4 =

1/x^2 + 4 + 2/x^2 + 4 =

then multiplied the top left numerator by the bottom right denominator and added the numerator to get:

x^2 + 6/x^2 + 4

is that the way its done?
• Nov 15th 2011, 03:51 PM
Quacky
Re: newby needing to know how to combine a natural number and an algebraic fraction
I'm extremely confused. Is it:

$\displaystyle 1+\frac{2}{x^2}+4$, or:

$\displaystyle 1+\frac{2}{x^2+4}$

The lack of brackets implies the former; your working out (and logic) implies the latter is actually the case, however.
• Nov 15th 2011, 04:36 PM
takatok
Re: newby needing to know how to combine a natural number and an algebraic fraction
Check out
http://www.mathhelpforum.com/math-he...orial-266.html
for info on how to make fractions look nice.

But given:
$\displaystyle 1+\frac{2}{x^2+4}$
you are correct.

$\displaystyle \frac{1}{1}*\frac{x^2+4}{x^2+4}+\frac{2}{x^2+4} =$

$\displaystyle \frac{x^2+4}{x^2+4}+\frac{2}{x^2+4} =$

$\displaystyle \frac{x^2+6}{x^2+4}$