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Question:

sloand92
sloand92
Student
High School - 12th Grade

Solve: x/x-1 = x/2 - (x+1)/(x+2)

Simplify: x^2+x-20/ (5x-20)

Multiply: (x^2-x-6)/(x^2+4x+3) *(times) (x^2-x-12)/(x^2-2x-8)

Please show step- by- step answers for all. Thank you.

I don't understand these and I would like to, please help!!

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Posted by sloand92 on Monday September 21, 2009 at 11:04 AM and tagged with algebra 2, math.

Answers:

  1. neela
    neela Teacher
    Graduate School

    eNotes Editor

    Solve:

    x/-1=x/2-(x+1)/(x+2).

    Go by pririty rules operations PEDMAS. RHS convert the fractions under the common denominator:

    1-1={x(x+2)-2(x+1)}/(x+2)

    Mutiply by the denominator, (x+2) both sides:

    0={x(x+2)-2(x+1)

    0=x^2+2x-2x-2

    0=x^2-2

    x^2=2

    x=sqrt(2)  or  x=-sqrt(2)

    Simplification:

    To simplify :x^2+x-20/(5x-20)= x^2+x-20/({5(x-4)}

    =x^2+x-4/(x-4). There is no further simplification.

    But if you intend x^2+x-20 is to be divided by (5x-20),Then it requires that you should write it like: (x^2+x-20)/(5x-20)

    Then, x^2+x-20=(x+5)(x-4) is dividendo

    (5x-20)= 5(x-4) is divisor. Therefore x^2+x-20 divided by 5x-20

    is (x^2+x-20)(5x-20)= (x+5)(x-4)/{5(x-4)}=(x+5)/5 or x/5+1

    Multiplication:

    (x^2-x-6)/(x^2+4x+3)*(x^2-x-12)/(x^2-2x+3)

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

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

    =(x+2){x-4)/(x+1)^2=(x^2-2x-8)/(x^2+2x+1)

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    Posted by neela on Monday September 21, 2009 at 12:24 PM