Question

How would I simplify this?

http://www.mathway.com/math_image.aspx?p=SMB02FSMB03SMB02FSMB032SMB10xSMB02fSMB03+SMB02FSMB033SMB10x-1SMB02fSMB03SMB101SMB102x-2SMB02fSMB03?p=56?p=82

Answer 1

\[\frac{\frac2x+\frac{3}{x-1}}{\frac{1}{2x-2}}=\left( \frac2x+\frac{3}{x-1} \right)\left( \frac{2x-2}{1} \right)\]

Answer 2

Find the LCM for the first term\[\frac 2x +\frac{3}{x-1}\]

Answer 3

See now that's what I keep getting, but the answer says its 10x-4/x?

Answer 4

My original answer was 2 though, because I cancelled x-1 from the top and bottom.

Answer 5

What is the LCD for\[\frac 2x +\frac{3}{x-1}\]

Answer 6

x-1

Answer 7

because of the 2 x's

Answer 8

Close, actually it is x(x-1) which means the expression can be written\[\frac 2x +\frac{3}{x-1}=\frac{2(x-1)+3x}{x(x-1)}\]

Answer 9

Oh, so then would I also x the 3x and the 2 to get 6x, then distribute?

Answer 10

I'm not sure what you are saying, but, yeah you would distribute and combine terms. Then multiply by (2x-2), etc.

Answer 11

K, thanks for the help.

Answer 12

\[\left( \frac2x+\frac{3}{x-1} \right)\left( \frac{2x-2}{1} \right)=\frac{(5x-2)2(x-1)}{x(x-1)}=\frac{10x-4}{x}\]

Answer 13

you're welcome.