Question

Simplify the complex rational expression

[ ( 6 / x-1 ) - ( 1 / x + 1) ] / [ ( x / x +1 ) + ( 1 / x + 1) ]

into a standard rational expression.

Answer 1

the denominator is 1

Answer 2

Start by finding a common denominator for the numerator
[6(x+1)/(x+1)(x-1)-(x+1)/(x+1)(x-1)]
6x+1-(x-1)/(x+1)(x-1)
5x+2/(x+1)(x-1)
the denominator just = 1
5x+2/(x^2-1)

Answer 3

\[\large \qquad \qquad \frac{\frac{6}{x-1} - \frac{1}{x+1}}{\frac{x}{x+1} + \frac{1}{x+1}}\]\[\large =\frac{\frac{6}{x-1} - \frac{1}{x+1}}{\frac{x}{x+1} + \frac{1}{x+1}} \cdot \frac{(x+1)(x-1)}{(x+1)(x-1)}\]\[\large =\frac{6(x+1) - (x-1)}{x(x-1) + (x-1)}\]\[\large = \frac{6x + 6 -x + 1}{x^2 - x + x - 1}\]\[\large =\frac{5x + 7}{x^2 - 1}\]

Answer 4

Taco, you forgot to distribute your 6

Answer 5

so It kept saying the dominator is incorrect.. :/

Answer 6

Hrm.. You got the same thing?

Answer 7

Yeah.. thats why it's saying the bottom one isn't right.

Answer 8

That's why I'm confused..

Answer 9

You wrote the problem incorrectly when you gave it to us.

Answer 10

It should have been x-1 in the left had denominator at the bottom.

Answer 11

Omg, I didn't even see that!

Answer 12

Thanks for telling me!

Answer 13

I wouldn't have known except that the screenshot showed the original problem ;)

Answer 14

LOL.. sorry.. I'm an idiot.. let me see..let me try to solve this.

Answer 15

Do you have skype, Polpak?

Answer 16

Sure thing. Clerical errors always burn me too.

Answer 17

GOT IT! Yess! Theehehee!!!!

Answer 18

Thank you all!