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Math Help - rational expressions

  1. #1
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    rational expressions

    my question is
    2x^2-5x+7 - x^2+3x-8
    x^2-2x-15 x^2-2x-15

    the common factor is (x-5)(x+3) but do still multiply the numerator with all of the denominator. or do i collect like terms. If i collect like terms i got
    3x^4+2x+1. and i cant factor that out
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  2. #2
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    Quote Originally Posted by jay123 View Post
    my question is
    2x^2-5x+7 - x^2+3x-8
    x^2-2x-15 x^2-2x-15

    the common factor is (x-5)(x+3) but do still multiply the numerator with all of the denominator. or do i collect like terms. If i collect like terms i got
    3x^4+2x+1. and i cant factor that out
    the denominator's are the same, just subtract the numerators and then simplify:

    \frac {2x^2 - 5x + 7}{x^2 - 2x - 15} - \frac {x^2 + 3x - 8}{x^2 - 2x - 15} = \frac {2x^2 - 5x + 7 - x^2 - 3x + 8}{x^2 - 2x - 15}

    now simplify the top, then factorize to see if anything cancels
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  3. #3
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    IM HAVING TROUBLE WITH THIS PROMBLEM...

    y+2 - y-4
    y-5 y+3... i changed the numerator's signs

    y-2 + y+4
    y-5 y+3 im confused on what i should do when i see that the demonators are different ... do i factor them out or do i mult each one by the num
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jay123 View Post
    IM HAVING TROUBLE WITH THIS PROMBLEM...

    y+2 - y-4
    y-5 y+3... i changed the numerator's signs

    y-2 + y+4
    y-5 y+3 im confused on what i should do when i see that the demonators are different ... do i factor them out or do i mult each one by the num
    no need to go there just yet. see post #5 here to see a quick method for adding fractions like these.

    after reading that, you should understand how i made the first step:

    \frac {y + 2}{y - 5} - \frac {y - 4}{y + 3} = \frac {(y + 2)(y + 3) - (y - 5)(y - 4)}{(y - 5)(y + 3)}

    now, expand the numerator and continue
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  5. #5
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    ok i understand that..
    i combine like terms and then i get this -4y+26
    (y-5)(y+3)
    i can factor out -2(2y-12) but i can factor out a 2 now. -2+2(y-6). what do i do with the -2+2 do i multiply it. -4(y-6).
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    Quote Originally Posted by jay123 View Post
    ok i understand that..
    i combine like terms and then i get this -4y+26
    (y-5)(y+3)
    i can factor out -2(2y-12) but i can factor out a 2 now. -2+2(y-6). what do i do with the -2+2 do i multiply it. -4(y-6).
    you made a mistake somewhere. most likely with the signs. your numerator should come out to 14y - 14
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  7. #7
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    hummm im still not getting the same answer ...i tried it about 6 times.
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  8. #8
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    Quote Originally Posted by jay123 View Post
    hummm im still not getting the same answer ...i tried it about 6 times.
    remember the minus sign between the two terms

     \frac {(y + 2)(y + 3) - (y - 5)(y - 4)}{(y - 5)(y + 3)} = \frac { \left( y^2 + 5y + 6 \right) - \left( y^2 -9y + 20 \right)}{(y - 5)(y + 3)}

    = \frac {y^2 + 5y + 6 - y^2 + 9y - 20}{(y - 5)(y + 3)}

    = \frac {14y - 14}{(y - 5)(y + 3)}

    = \frac {14(y - 1)}{(y - 5)(y + 3)}
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  9. #9
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    thanks.

    I did this problem but i keep getting it wrong. can you see the problem?
    x-3 + x-1
    x^2+3x+2 x^2-4

    x-3 + x-1 = (x-3)(x-2) + (x-1)(x+1) = x^2-5x+x^2-1
    (x+1)(x+2) (x-2)(x+2) (x+1)(x+2)(x-2) (x+1)(x+2)(x-2)

    = 2x^2-5x-7
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  10. #10
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    Quote Originally Posted by jay123 View Post
    thanks.

    I did this problem but i keep getting it wrong. can you see the problem?
    x-3 + x-1
    x^2+3x+2 x^2-4

    x-3 + x-1 = (x-3)(x-2) + (x-1)(x+1) = x^2-5x+x^2-1
    (x+1)(x+2) (x-2)(x+2) (x+1)(x+2)(x-2) (x+1)(x+2)(x-2)...
    there should be a +6 in the numerator of the last fraction that isn't there

    and how did you get your last line to be like that?
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  11. #11
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    isnt difference of squares x^2-4 (x-2)(x+2)

    x^2+3x2 + x^2-4 = isnt this diff. of squares..
    (x+2)(x+1)
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  12. #12
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    Quote Originally Posted by jay123 View Post
    isnt difference of squares x^2-4 (x-2)(x+2)

    x^2+3x2 + x^2-4 = isnt this diff. of squares..
    (x+2)(x+1)
    i don't understand what you're saying. please be more clear.
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  13. #13
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    x^2-4. this is difference of squares right? (x-2)(x+2)= x^2-4
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  14. #14
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    Quote Originally Posted by jay123 View Post
    x^2-4. this is difference of squares right? (x-2)(x+2)= x^2-4
    yes, but that was not the issue here. that's not where you went wrong
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