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Simplify. Express your answer as a single fraction in simplest form. \newlinez5−310z\frac{z}{5} - \frac{3}{10}z

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newlinez5−310z\frac{z}{5} - \frac{3}{10}z
  1. Identify common denominator: Identify the common denominator for the fractions z5\frac{z}{5} and 310z\frac{3}{10z}. Since the denominators are 55 and 10z10z, the least common denominator (LCD) is 10z10z.
  2. Rewrite fractions with LCD: Rewrite each fraction with the common denominator of 10z10z. For the first fraction, multiply both the numerator and denominator by 2z2z to get (2z⋅z)/(5⋅2z)=2z2/10z(2z \cdot z)/(5 \cdot 2z) = 2z^2/10z. For the second fraction, multiply both the numerator and denominator by 11 to get (3⋅1)/(10z⋅1)=3/10z(3 \cdot 1)/(10z \cdot 1) = 3/10z.
  3. Combine fractions: Combine the fractions over the common denominator.\newline(2z210z)−(310z)=2z2−310z(\frac{2z^2}{10z}) - (\frac{3}{10z}) = \frac{2z^2 - 3}{10z}
  4. Simplify expression: Simplify the expression, if possible.\newlineThe numerator 2z2−32z^2 - 3 cannot be simplified further, and the denominator 10z10z is already in simplest form.\newlineTherefore, the final simplified expression is (2z2−3)/10z(2z^2 - 3)/10z.

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