Algebra

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1. Subtract and simplify
18/y-8 - 18/8-y
2. subtract simplify if possible
v-5/v - 7v-31/11v

3. Simplify by removing factors of 1
r^2-81/(r+9)^2

4. Divide and simplify
v^2-16/25v+100 divided by v-4/20

5. find all rational numbers for which the rational expression is undefined:
-18/7w

6. solve:
2/Z+4= 1/z-6

  • Algebra -

    1. 18 / (y - 8) - 18 / (8 - y),
    Multiply numerator and denominator of
    2nd fraction by -1 and get:

    18 / (y - 8) + 18 / (y - 8) =
    36 / (y - 8).

    2. (v - 5) / v - (7v - 31) / 11v,
    Common denominator = 11v:
    (11v - 55 -7v + 31) / 11v,
    Combine like-terms:
    (4v - 24) / 11v = 4(v - 6) / 11v.

    3. (r^2 - 81) / (r + 9)^2,
    Factor the numerator:
    (r + 9) (r - 9) / (r + 9)^2,
    Multiply numerator and denomjnator by
    (r + 9)^2 and get:

    (r + 9)^-1 (r - 9) / 1,
    Multiply numerator and denominator by
    (r + 9)^1:

    (r - 9) / (r + 9).

    4. (v^2 - (16/25)v + 100) / (v - 4)/20
    Multiply numerator and denominator by 25 and get:
    (V^2 - 16V + 100) / 5(V - 4) / 4,

    Multiply numerator and denominqator by
    4/5 and get:
    4/5(v^2 - 16v + 100) / (v - 4).

    6. 2 / (z + 4) = 1 / (z - 6),
    Cross multiply:
    2z - 12 = z + 4,
    2z - z = 4 + 12,
    z = 16.

  • Algebra -

    _4y_____ _ ___3y________
    y^2+6y+5 y^2+5y+4

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