Monday

December 22, 2014

December 22, 2014

Posted by **Kate** on Tuesday, January 5, 2010 at 9:58pm.

Thanks for all of the help guys. I really appreciate it.

I was woudnering if you could show me how to do this step by step and the thought process that goes through your head while you do this. This way I will be able to try to solve some of these problems on my own becasue I really have no idea how to do them.

Perform the indicated operation and simplify the ersult. Leave your anser in factored form.

1/x - 2/(x^2 + x) + 3/(x^3 - x^2)

THANK YOU!!!

- Precalculus -
**Reiny**, Tuesday, January 5, 2010 at 10:13pmremember to add/subtract fractions we need a common denominator.

let's write our expression in factored form

1/x - 2/(x^2 + x) + 3/(x^3 - x^2)

= 1/x - 2/[x(x+1)] + 3/[x^2(x-1)]

so the common denominator is x^2(x+1)(x-1)

first term: x(x+1)(x-1)/[x^2(x+1)(x-1)]

notice if we cancel we get 1/x

second term: -2x(x-1)/[x^2(x+1)(x-1)]

again, see what you get when you cancel

third term: 3(x+1)/[x^2(x+1)(x-1)]

so we get

[x(x+1)(x-1) - 2x(x-1) + 3(x+1)]/[x^2(x+1)(x-1)]

I will let you finish it,

(I got (x^3 - 2x^2 + 4x + 3)/[x^2(x^2 - 1)]

- Precalculus -
**Damon**, Tuesday, January 5, 2010 at 10:23pmI bet you have a sign wrong but will do as shown.

1/x

-2/[x(x+1)]

+3/[x^2(x-1)]

we need a common denominator

need LCD = x^2 (x-1)(x+1) = x^2(x^2-1)

so

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

-2 [ (x)(x-1) ] /LCD

+3 [ (x+1 ] / LCD

then

[1 (x(x^2-1) -2 (x^2-x) +3 (x+1) ]/LCD

[ x^3-x -2x^2 +2x +3x+3 ]/LCD

(x^3 -2x^2 +4x +3)/[x^2(x^2-1)]

I could not simplify, suspct mistake but that is the idea.

- Precalculus -
**Damon**, Tuesday, January 5, 2010 at 10:24pmOh, I see Reiny got the same answer. If you typed it right the answer is right.

**Answer this Question**

**Related Questions**

Math - Algebra II - Hello, i'm currently doing functions and I was fine until I ...

Maths! - Find the sum of all multiples of 5 between 100 and 300 inclusive. Ans: ...

Math !!!!!!!! - Ok i have a Summer Math Assignment & i really need help on this...

Algebra help - f(x)=x^3-4x^2-x+4 How do I find the x-intercept for this? This is...

chemistry - How many moles of ammonium ions are in 8.794g of ammonium carbonate...

chemistry step by step for me thank a lot - What is the weight of ca(oh)2 ...

Chemistry - When 100mL of 1.00 M Ba (NO3)2 and 100 mL of 1.00 M Na2SO4, both at ...

algebra 2 - A. I need to write an equation to the linear equation..(-2,-2), (3,3...

Algebra 2 - V=df-di/tf-ti; solve for ti Literal equations! I would really ...

math - how do you solve the exponential equation, 12^x = 14^3x? If someone could...