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(4xy)/(2) = (4)/(2)xy

Mathematics

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Step-by-step solution

24 steps

Here are the simplifications for each expression:

Part 1.1· 2 steps

  1. Divide the numerical coefficients.

    4xy2=42xy\frac{4xy}{2} = \frac{4}{2}xy

  2. Simplify the fraction.

    2xy2xy

    The simplified expression is 2xy\boxed{\mathbf{2xy}}.

Part 1.2· 2 steps

  1. Divide the numerical coefficients and the variables.

    15a3a=153⋅aa\frac{15a}{3a} = \frac{15}{3} \cdot \frac{a}{a}

  2. Simplify the terms.

    5⋅1=55 \cdot 1 = 5

    The simplified expression is 5\boxed{\mathbf{5}}.

Part 1.3· 2 steps

  1. Divide the numerical coefficients and the variables.

    18m312m=1812⋅m3−1\frac{18m^3}{12m} = \frac{18}{12} \cdot m^{3-1}

  2. Simplify the fraction and the exponent.

    32m2\frac{3}{2}m^2

    The simplified expression is 32m2\boxed{\mathbf{\frac{3}{2}m^2}}.

Part 1.4· 3 steps

  1. Simplify the numerator and the denominator separately.

    (3x3)23x3+3x3=32(x3)26x3\frac{(3x^3)^2}{3x^3+3x^3} = \frac{3^2(x^3)^2}{6x^3}

  2. Perform the exponentiation and addition.

    9x66x3\frac{9x^6}{6x^3}

  3. Divide the numerical coefficients and the variables.

    96x6−3=32x3\frac{9}{6}x^{6-3} = \frac{3}{2}x^3

    The simplified expression is 32x3\boxed{\mathbf{\frac{3}{2}x^3}}.

Part 1.5· 3 steps

  1. Simplify the numerator by combining like terms and the denominator by applying the exponent.

    −x5−2x5(−3x2)2=(−1−2)x5(−3)2(x2)2\frac{-x^5-2x^5}{(-3x^2)^2} = \frac{(-1-2)x^5}{(-3)^2(x^2)^2}

  2. Perform the operations.

    −3x59x4\frac{-3x^5}{9x^4}

  3. Divide the numerical coefficients and the variables.

    −39x5−4=−13x\frac{-3}{9}x^{5-4} = -\frac{1}{3}x

    The simplified expression is −13x\boxed{\mathbf{-\frac{1}{3}x}}.

Part 2.1· 2 steps

  1. Factor out the common term from the numerator.

    3x+63=3(x+2)3\frac{3x+6}{3} = \frac{3(x+2)}{3}

  2. Cancel out the common factor.

    x+2x+2

    The simplified expression is x+2\boxed{\mathbf{x+2}}.

Part 2.2· 2 steps

  1. Factor out the common term from the numerator.

    4a+124=4(a+3)4\frac{4a+12}{4} = \frac{4(a+3)}{4}

  2. Cancel out the common factor.

    a+3a+3

    The simplified expression is a+3\boxed{\mathbf{a+3}}.

Part 2.3· 2 steps

  1. Factor out the common term from the numerator.

    x2+6xx=x(x+6)x\frac{x^2+6x}{x} = \frac{x(x+6)}{x}

  2. Cancel out the common factor.

    x+6x+6

    The simplified expression is x+6\boxed{\mathbf{x+6}}.

Part 2.4· 3 steps

  1. Factor out the common term from the numerator.

    4a3+12a24a=4a2(a+3)4a\frac{4a^3+12a^2}{4a} = \frac{4a^2(a+3)}{4a}

  2. Cancel out the common factor $4a$.

    a(a+3)a(a+3)

  3. Distribute the aa (optional, but often preferred).

    a2+3aa^2+3a

    The simplified expression is a2+3a\boxed{\mathbf{a^2+3a}}.

Part 2.5· 3 steps

  1. Divide each term in the numerator by the denominator.

    3p5−15p4−9p33p2=3p53p2−15p43p2−9p33p2\frac{3p^5-15p^4-9p^3}{3p^2} = \frac{3p^5}{3p^2} - \frac{15p^4}{3p^2} - \frac{9p^3}{3p^2}

  2. Simplify each term using exponent rules.

    p5−2−5p4−2−3p3−2p^{5-2} - 5p^{4-2} - 3p^{3-2}

  3. Perform the subtractions in the exponents.

    p3−5p2−3pp^3 - 5p^2 - 3p

    The simplified expression is p3−5p2−3p\boxed{\mathbf{p^3-5p^2-3p}}.

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