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Multiplying and Dividing Rational Expressions:

2) x^2-8x+7/x^2+6x-7 = (x-7)/(x+7)

3) x^2-5x+6/x+4 times 3x+12/x-2 =3(x-3)

4)2x-3/5x+1 divided by 6x^2-13x+6/15x^2-7x-2=1

5) x^3-9x/x^2+11x+24 times x^2+7x-8/x^2-4x+3= x(x-3)(x-1)/(x+3)(x+8)

6) 4x-8/x^2-x-6 divided by x^3 +x^2-6x/x^2-9=(x-3)/x(x-2)

7) x^2-16/x-3 divided x+4/x^2-9=(x-1)/(x+1)

  • math - ,

    are they correct?

  • math - ,

    4. (2X-3)/(4X-1) -Div by (6X^2-13X+6)/
    Factor trinomial in numerator using A*C Method:
    A*C = 6*6 = 36 = -4*-9,
    6X^2 -4X-9X +6
    Group the 4 terms in pairs and factor each pair:
    2X(3X-2) -3(3X-2). Factor out (3x-2):
    (3X-2) (2X-3).

    Factor the trinomial in denominator
    using A*C Method:
    A*C = 15*-2 =-30 = 3*-10.
    15X^2 +3X-10X -2.
    Group the 4 terms in pairs and factor each pair:
    3x(SX+1) -3(5X+1), Factor out (5x+1):
    (5X+1) (3X-2).

    Write original expression in factored form:
    (2X-3)/(5X+1) Div by (3X-2)(2X-3)/
    Cancel the (3X-2) factors:
    (2X-3)/5X+1) Div by (2X-3)/(5X+1).
    Invert divisor and multiply:
    (2X-3)/(5X+1) * (5X+1)/(2X-3).
    Cancel the (5X+1) factors:
    (2X-3)/(2X-3) = 1.

  • math - ,

    5. (X^3-9)/(X^2+11X+24) * (X^2+7X-8_/
    (X^2-4X+3) =
    Factor both numerators & denominators:
    X(X^2-9)/(X+3)(X+8) * (X-1)(X+8)/
    (X-1)(X-3) =
    Cancel factors (X+8), and (X-1).
    X(X^2-9)/(X+3) * 1/(X-3)
    Factor (X^2-9):
    X(X+3)(X-3)/(X+3) * 1/(X-3).
    Cancel factors (x+3) & (X-3):
    = X.

  • math - ,

    6.(4X -8)/(X^2 -X -6) Div (X^3+X^26X)/
    Factor completely:
    4(X-2)/(X-3)(X+2) Div X(X^2+X-6)/(X+3)

    4(X-2)/(X-3)(X+2) Div X(X+3)(X-2)/(X+3)(X-3).
    Cancel factor (X+3) and invert divisor
    4(X-2)/(X-3)(X+2) * (X-3)/X(X-2).
    Cancel factors (X-2), (Z-3)

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