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Simplify the following algebraic fractions: i) 7m/8 - 7m/12 ii) (4x+2)/12 - (3x+2)/8

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2 parts
i

7m24\frac{7m}{24}

ii

−x+224-\frac{x+2}{24}

Step-by-step solution

7 steps

Here are the simplified expressions:

Part i· 3 steps

Simplify 7m8−7m12\frac{7m}{8} - \frac{7m}{12}

  1. Find the least common multiple (LCM) of the denominators 8 and 12.

    The multiples of 8 are 8, 16, 24, 32, ...
    The multiples of 12 are 12, 24, 36, ...
    The LCM of 8 and 12 is 24.

  2. Rewrite each fraction with the common denominator.

    7m8=7m×38×3=21m24\frac{7m}{8} = \frac{7m \times 3}{8 \times 3} = \frac{21m}{24} 7m12=7m×212×2=14m24\frac{7m}{12} = \frac{7m \times 2}{12 \times 2} = \frac{14m}{24}

  3. Subtract the fractions.

    21m24−14m24=21m−14m24\frac{21m}{24} - \frac{14m}{24} = \frac{21m - 14m}{24} =7m24= \frac{7m}{24}

    The simplified expression is 7m24\boxed{\frac{7m}{24}}.

Part ii

−x+224-\frac{x+2}{24}

Simplify 4x+212−3x+28\frac{4x+2}{12} - \frac{3x+2}{8}

  1. Find the least common multiple (LCM) of the denominators 12 and 8.

    The LCM of 12 and 8 is 24.

  2. Rewrite each fraction with the common denominator.

    4x+212=(4x+2)×212×2=8x+424\frac{4x+2}{12} = \frac{(4x+2) \times 2}{12 \times 2} = \frac{8x+4}{24} 3x+28=(3x+2)×38×3=9x+624\frac{3x+2}{8} = \frac{(3x+2) \times 3}{8 \times 3} = \frac{9x+6}{24}

  3. Subtract the fractions.

    Remember to distribute the negative sign to all terms in the second numerator.

    8x+424−9x+624=(8x+4)−(9x+6)24\frac{8x+4}{24} - \frac{9x+6}{24} = \frac{(8x+4) - (9x+6)}{24} =8x+4−9x−624= \frac{8x+4 - 9x - 6}{24}

  4. Combine like terms in the numerator.

    =(8x−9x)+(4−6)24= \frac{(8x - 9x) + (4 - 6)}{24} =−x−224= \frac{-x - 2}{24}

    This can also be written as:

    =−x+224= -\frac{x+2}{24}

    The simplified expression is −x+224\boxed{-\frac{x+2}{24}}.

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