airyana1114
  • airyana1114
I need help with finding the simplified form of an equation.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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airyana1114
  • airyana1114
\[ \frac{ 1 }{ x } - \frac{ 2 }{ x^{2}+ x }\]
DanJS
  • DanJS
to combine the two, need to change to same denominators
DanJS
  • DanJS
x^2 +6 x = 2z + 6 for

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airyana1114
  • airyana1114
I'm sorry where did the 6 and z come from?
AlexandervonHumboldt2
  • AlexandervonHumboldt2
like dan said, equal the denominators
mathmale
  • mathmale
Please look at the expression you've typed in, and determine what the lowest common denominator (LCD) is. You'll need the LCD to combine those two fractions into one.
AlexandervonHumboldt2
  • AlexandervonHumboldt2
hint: x^2+x=x*(x+1)
mathmale
  • mathmale
To find the LCD, you could multiply the two given denominators together. but Alex has a better idea: He sees that the two given denominators share a common factor, which is x. The den. of the second fract. is done (although it'd look nicer if you factor it as Alex has done). What do y ou have to do to the 1st fraction to obtain the same LCD in the denominator? Hint: You must multiply its numerator and its denom. by the same thing.
airyana1114
  • airyana1114
I'm not sure what I would do, all I know is that I need to get \[x^{2}\] into my first denominator.
mathmale
  • mathmale
It's more than just x^2. If done correctly, your numerator in the first fraction will become a polynomial in x.
mathmale
  • mathmale
Note that you have "x" in the denom. of the first fraction. Multiply that x by ... what? ... so that you have the LCD in BOTH fractions.
airyana1114
  • airyana1114
by two?
mathmale
  • mathmale
First, type in the LCD. See Alex's work (above). Second, determine by what quantiity you must multiply the x in the denom. of the 1st question to get the LCD there.
airyana1114
  • airyana1114
So my denominator's would be x(x + 1)?
airyana1114
  • airyana1114
To get that for my first denominator I need to multiply x by (x + 1), correct?
mathmale
  • mathmale
yes, very good. if you mult
mathmale
  • mathmale
the den. of the 1st fract. by x+1, you must also mult. the num. by the same quantity. Do this and type in your results, please.
mathmale
  • mathmale
Thus, \[\frac{ 1 }{ x }+\frac{ 2 }{ x^2+x }becomes. what?\]
airyana1114
  • airyana1114
would my x^2 + x become x(x + 1) as well?
mathmale
  • mathmale
The second fraction doesn't change, unless y ou wish to factor the denom. (which looks better). The first fraction becomes
mathmale
  • mathmale
\[\frac{ x+1 }{ x(x+1) }\]
mathmale
  • mathmale
And now the fractions have the same denominator.
airyana1114
  • airyana1114
Okay, so then what happens with my second numerator?
mathmale
  • mathmale
Nothing. No need to change it, because the denom of that fraction is already the LCD. Now combine those two fractions, now that they have the same denom. This requires that y ou add together the numerators. Be careful with signs.
airyana1114
  • airyana1114
Okay so I first changed my denominators to x(x + 1), then I change my first numerator by multiply it by (x + 1) which gives me \[\frac{ x+1 }{ x(x+1) }\] and then I just subtract my second numerator from my first correct? Since in my original equation I was subtracting?
airyana1114
  • airyana1114
Which leaves me with x-1 over x(x+1)
mathmale
  • mathmale
Great job!!!!
airyana1114
  • airyana1114
:) thank you!
mathmale
  • mathmale
Hope you'll review our discussion so that you can apply this procedure to solving similar problems in the future. You're welcome!!

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