Question

I need help with finding the simplified form of an equation.

Answer 1

\[ \frac{ 1 }{ x } - \frac{ 2 }{ x^{2}+ x }\]

Answer 2

to combine the two, need to change to same denominators

Answer 3

x^2 +6 x = 2z + 6 for

Answer 4

I'm sorry where did the 6 and z come from?

Answer 5

like dan said, equal the denominators

Answer 6

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.

Answer 7

hint:
x^2+x=x*(x+1)

Answer 8

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.

Answer 9

I'm not sure what I would do, all I know is that I need to get \[x^{2}\] into my first denominator.

Answer 10

It's more than just x^2. If done correctly, your numerator in the first fraction will become a polynomial in x.

Answer 11

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.

Answer 12

by two?

Answer 13

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.

Answer 14

So my denominator's would be x(x + 1)?

Answer 15

To get that for my first denominator I need to multiply x by (x + 1), correct?

Answer 16

yes, very good. if you mult

Answer 17

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.

Answer 18

Thus, \[\frac{ 1 }{ x }+\frac{ 2 }{ x^2+x }becomes. what?\]

Answer 19

would my x^2 + x become x(x + 1) as well?

Answer 20

The second fraction doesn't change, unless y ou wish to factor the denom. (which looks better). The first fraction becomes

Answer 21

\[\frac{ x+1 }{ x(x+1) }\]

Answer 22

And now the fractions have the same denominator.

Answer 23

Okay, so then what happens with my second numerator?

Answer 24

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.

Answer 25

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?

Answer 26

Which leaves me with x-1 over x(x+1)

Answer 27

Great job!!!!

Answer 28

:) thank you!

Answer 29

Hope you'll review our discussion so that you can apply this procedure to solving similar problems in the future. You're welcome!!