Question

I need help with these questions please.

FInd the LCM of x^2 + 10x , x^2 - 10x

I will draw other ones below

Answer 1

factor x^2 + 10x to get ______

Answer 2

x(x + 10)

Answer 3

factor x^2 - 10x to get _____

Answer 4

x(x - 10)

Answer 5

the unique factors are: x, x+10, x-10

Answer 6

multiply all of these unique factors to get x(x+10)(x-10)

Answer 7

and that's the LCM (factored out)

Answer 8

you can choose to expand it out, but you're pretty much done

Answer 9

wow thank you! Could you help me with two others?

Answer 10

sure

Answer 11

I can help

Answer 12

\[Solve R = \frac{ gy }{ g + y } for y \]

Answer 13

\[\Large R = \frac{ gy }{ g + y }\]


\[\Large R(g+y) = gy\]


\[\Large Rg+Ry = gy\]


\[\Large Rg = gy-Ry\]


\[\Large Rg = (g-R)y\]


See what to do from here?

Answer 14

I need to get y alone for I would divide both sides by (g - R)??

Answer 15

exactly, so you would get


\[\Large R = \frac{ gy }{ g + y }\]


\[\Large R(g+y) = gy\]


\[\Large Rg+Ry = gy\]


\[\Large Rg = gy-Ry\]


\[\Large Rg = (g-R)y\]


\[\Large \frac{Rg}{g-R} = y\]


\[\Large y = \frac{Rg}{g-R}\]

Answer 16

\[Simplify the expression leave \in factored form. \frac{ 2y }{ y(2y - 1) } + \frac{ 1 }{ 2y - 1 }\]

Answer 17

I'll get you started

Answer 18

Thanks

Answer 19

the LCD is y(2y - 1), so you need to get each denominator equal to the LCD

the first denominator is already there, so no need to worry about the first fraction

the second denominator is not equal to the LCD, so you need to multiply top and bottom by 'y' to get to the LCD

Answer 20

so you'll go from

\[\Large \frac{ 2y }{ y(2y - 1) } + \frac{ 1 }{ 2y - 1 }\]

to

\[\Large \frac{ 2y }{ y(2y - 1) } + \frac{ y }{ y(2y - 1) }\]

Answer 21

the denominators are now equal, which means you can add the two fractions

Answer 22

tell me what you get

Answer 23

\[\frac{ 3y }{ y(2y - 1) } ?\]

Answer 24

now the y terms will cancel leaving you with

\[\Large \frac{ 3 }{ 2y - 1}\]

Answer 25

Cool.. Thank you for your help!

Answer 26

you're welcome

Answer 27

If I ever have another question could I ask you?
I like how you help but also let me work on the problem

Answer 28

sure I'd love to help you out if you have another question

Answer 29

\[Solve and Check \frac{ 3 }{ 1 - x } = \frac{ 4 }{ 1 + x }\]

Answer 30

I rewrote it as 3(1 + x) = 4(1 - x) but than I am not sure where to go from there

Answer 31

You want to isolate x, so you have to get all the x terms to one side (and everything else to the other)


3(1 + x) = 4(1 - x)

3 + 3x = 4 - 4x ... distribute

3+3x + 4x = 4

3x+4x = 4 - 3

what's next?

Answer 32

Wouldnt it be

3 + 3x = 4 - 4x

3 + 3x + 4x = 4

3 + 7x = 4
-3 -3

7x = 1

x = 1/7

Answer 33

good

3x+4x = 4-3

7x = 1

x = 1/7

Answer 34

Thank you! That is it for now. I will be back again next Sunday! Hope to see you here.

Answer 35

you're welcome, cya later and have a good night

Answer 36

Thank you, You too