Question

how does (x+1)/[x(x-1)] - 1/[2(x-1)] = (x+2)/[2x(x-1)]?

Answer 1

\[\frac{ x+1 }{ x(x-1) } - \frac{ 1 }{ 2(x-1) } = \frac{ x+2 }{ 2x(x-1) }\]

Answer 2

okay, what you are going to do first is the parenthses. distribute x to x and -1.

Answer 3

x * x is x^2, and x * -1 is -1x. so now type the equation you now have.

Answer 4

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

Answer 5

okay, good. now distribute 2 to x and -1. 2 * x is 2x, and -1 * 2 is -2. type the equation you have now.

Answer 6

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

Answer 7

nice. now distribute 2x to x and -1. 2x * x is 2x^2, and 2x * -1 is-2x. type the equation you have now.

Answer 8

\[\frac{ x+1 }{ x^2-x }-\frac{ 1 }{ 2x-2 } = \frac{ x+2 }{ 2x^2-2x }\]
ah about that, I just put that in the right hand side because that's what I want the left hand side to turn out to

Answer 9

err... what?

Answer 10

It tells me to prove the left hand side to equal the right hand side

Answer 11

Also, doing the left hand side gives me x+2 but what I want to know is why is 2x(x-1) on the bottom?

Answer 12

There are two fractions on the left, and you want to get a common denominator! You know you can multiply anything by the number 1, correct? Well there are some tricky ways of representing the number 1, for instance: \[\Large \frac{x}{x}=1 \] So you can multiply by 1 in this tricky way to get the denominators to match the right side.

Answer 13

hmm I'm very sorry, I may have worded my question wrong.
I'll explain in detail what I want to figure out.
\[\frac{ x+1 }{ x(x-1) }-\frac{ 1 }{ 2(x-1) } = \frac{ x+2 }{ 2x(x-1) }\]
I don't know what this process is called but please bear with me if you don't know
\[2x(x-1)(\frac{ x+1 }{ x(x-1) }-\frac{ 1 }{ 2(x-1) }) = \frac{ x+2 }{ 2x(x-1) }\]
\[2(x+1)-x(1) = \frac{ x+2 }{ 2x(x-1) }\]
2x + 2 - x = \frac{ x+2 }{ 2x(x-1) }
\[2x + 2 - x = \frac{ x+2 }{ 2x(x-1) }\]
\[x+2 = \frac{ x+2 }{ 2x(x-1) }\]
Now on the right hand side, you the thing I used to divide the fractions are on the bottom of x+2 which also appears on the left hand side

Answer 14

why is it there*