3 ms·

all right the brackets concept makes sense. remembering a/b + c/d = (ad+bc)/bd A/(x+2) + B/(1-x+x^2) = A(1-x+x^2) + B(x+2)/(x+2)(1-x+x^2) correct??

by pencil 16y ago

RiderOfGiraffes 16y ago
Yes, except you forgot the brackets again. You should have: [ A(1-x+x^2) + B(x+2) ] / [ (x+2)(1-x+x^2) ] You probably knew that, but this is really, really important. Not getting it right now will confuse you a great deal later. However, now you have this as your numerator: A(1-x+x^2) + B(x+2) [Eqn *] Look again at your original problem - what do you want the numerator to be? - Expand out Eqn * to remove the brackets. - What values can you assign to A and B to make Eqn * be the numerator you want? As a hint, A and B are not simply numbers.
- pencil 16y ago
  first of all i don't know the significance of replacing the numerator with capital letters when decomposing partial fractions.i'am not aware of the practical implications of these problems.all i know is it'll come in handy when solving laplace transforms in the future which is used in physics/electrical etc.(that's what i'am after). and if you are curious to know why i wanna learn these..well i don't have a proper reason.i simply want to!! i looked back at the original problem but i'am unable to figure out the values to assign to A and B.
  - RiderOfGiraffes 16y ago
    OK, to recap. You want to decompose this: [ 3x-1 ] / [ (x+2)(1-x+x^2) ] into fractions. In other words, you want to find A and B such that: A/(x+2) + B/(1-x+x^2) = [ 3x-1 ] / [ (x+2)(1-x+x^2) ] Apart from getting the brackets wrong, you said (correctly) that the left hand side is equal to this: [ A(1-x+x^2) + B(x+2) ] / [ (x+2)(1-x+x^2) ] So now you need to solve: [ A(1-x+x^2)+B(x+2) ] / [ (x+2)(1-x+x^2) ] = (3x-1) / [ (x+2)(1-x+x^2) ] The denominators are equal, so you just need to make the numerators equal. So tell me - what equation do you have to solve?
    - pencil 16y ago
      i get A(1-x+x^2) + B(x+2) = 3x-1
      - RiderOfGiraffes 16y ago
        Excellent. + Expand B(x+2) + Expand A(1-x+x^2) What do you get? You need to play with these sorts of equations and see what happens - see what you get.
        pencil 16y ago
        expand B(x+2)?? but how??
        RiderOfGiraffes 16y ago
        How would you expand 3(x+2)?
        pencil 16y ago
        3x+6
        RiderOfGiraffes 16y ago
        Or, before simplifying, 3x+3.2 (using a dot for multiplication) So how do you expand B(x+2) ?
        pencil 16y ago
        Bx+B2 ??? now it's getting funny!!!!!!!!
        RiderOfGiraffes 16y ago
        So going back, you need to solve: [ A(1-x+x^2)+B(x+2) ] / [ (x+2)(1-x+x^2) ] = (3x-1) / [ (x+2)(1-x+x^2) ] As I said, the denominators are already equal, so you need to make the numerators equal. That means you need to make this: A(1-x+x^2)+B(x+2) equal to (3x-1). Expand this - you already know that the second part becomes B.x+2B - and have a look. Then think - what can you set A and B to be to make it equal to 3x-1? What if you set A to be x? What if you set B to be 2? What if you set A to be -3? What if you set B to be 2x? Try those, try more, see if you can work out how you can get 3x-1. Here's a hint: when you expand you'll get one of the terms as Ax^2. How can you get that to cancel out? Try things. Tell me what you see, tell me what you get.

all right the brackets concept makes sense. remembering a/b + c/d = (ad+bc)/bd A/(x+2) + B/(1-x+x^2) = A(1-x+x^2) + B(x+2)/(x+2)(1-x+x^2) correct??

by pencil 16y ago

all right the brackets concept makes sense. remembering a/b + c/d = (ad+bc)/bd A/(x+2) + B/(1-x+x^2) = A(1-x+x^2) + B(x+2)/(x+2)(1-x+x^2) correct??

RiderOfGiraffes 16y ago

Yes, except you forgot the brackets again. You should have: [ A(1-x+x^2) + B(x+2) ] / [ (x+2)(1-x+x^2) ] You probably knew that, but this is really, really important. Not getting it right now will confuse you a great deal later. However, now you have this as your numerator: A(1-x+x^2) + B(x+2) [Eqn *] Look again at your original problem - what do you want the numerator to be? - Expand out Eqn * to remove the brackets. - What values can you assign to A and B to make Eqn * be the numerator you want? As a hint, A and B are not simply numbers.

pencil 16y ago
first of all i don't know the significance of replacing the numerator with capital letters when decomposing partial fractions.i'am not aware of the practical implications of these problems.all i know is it'll come in handy when solving laplace transforms in the future which is used in physics/electrical etc.(that's what i'am after). and if you are curious to know why i wanna learn these..well i don't have a proper reason.i simply want to!! i looked back at the original problem but i'am unable to figure out the values to assign to A and B.
- RiderOfGiraffes 16y ago
  OK, to recap. You want to decompose this: [ 3x-1 ] / [ (x+2)(1-x+x^2) ] into fractions. In other words, you want to find A and B such that: A/(x+2) + B/(1-x+x^2) = [ 3x-1 ] / [ (x+2)(1-x+x^2) ] Apart from getting the brackets wrong, you said (correctly) that the left hand side is equal to this: [ A(1-x+x^2) + B(x+2) ] / [ (x+2)(1-x+x^2) ] So now you need to solve: [ A(1-x+x^2)+B(x+2) ] / [ (x+2)(1-x+x^2) ] = (3x-1) / [ (x+2)(1-x+x^2) ] The denominators are equal, so you just need to make the numerators equal. So tell me - what equation do you have to solve?
  - pencil 16y ago
    i get A(1-x+x^2) + B(x+2) = 3x-1
    - RiderOfGiraffes 16y ago
      Excellent. + Expand B(x+2) + Expand A(1-x+x^2) What do you get? You need to play with these sorts of equations and see what happens - see what you get.
      - pencil 16y ago
        expand B(x+2)?? but how??
        RiderOfGiraffes 16y ago
        How would you expand 3(x+2)?
        pencil 16y ago
        3x+6
        RiderOfGiraffes 16y ago
        Or, before simplifying, 3x+3.2 (using a dot for multiplication) So how do you expand B(x+2) ?
        pencil 16y ago
        Bx+B2 ??? now it's getting funny!!!!!!!!
        RiderOfGiraffes 16y ago
        So going back, you need to solve: [ A(1-x+x^2)+B(x+2) ] / [ (x+2)(1-x+x^2) ] = (3x-1) / [ (x+2)(1-x+x^2) ] As I said, the denominators are already equal, so you need to make the numerators equal. That means you need to make this: A(1-x+x^2)+B(x+2) equal to (3x-1). Expand this - you already know that the second part becomes B.x+2B - and have a look. Then think - what can you set A and B to be to make it equal to 3x-1? What if you set A to be x? What if you set B to be 2? What if you set A to be -3? What if you set B to be 2x? Try those, try more, see if you can work out how you can get 3x-1. Here's a hint: when you expand you'll get one of the terms as Ax^2. How can you get that to cancel out? Try things. Tell me what you see, tell me what you get.