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Divide. Write your answer in simplest form. \newline52g÷(2g−3)\frac{5}{2g} \div (2g - 3)

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Multiply and divide rational expressionsright chevron icon

Full solution

Q. Divide. Write your answer in simplest form. \newline52g÷(2g−3)\frac{5}{2g} \div (2g - 3)
  1. Rewrite Division as Multiplication: Rewrite the division as a multiplication by taking the reciprocal of the divisor. So, 52g÷(2g−3)\frac{5}{2g} \div (2g - 3) becomes 52g×1(2g−3)\frac{5}{2g} \times \frac{1}{(2g - 3)}.
  2. Multiply Numerators and Denominators: Multiply the numerators and then multiply the denominators. So, 52g×1(2g−3)\frac{5}{2g} \times \frac{1}{(2g - 3)} becomes (5×1)(2g×(2g−3))\frac{(5 \times 1)}{(2g \times (2g - 3))}.
  3. Simplify Numerator and Expand Denominator: Simplify the numerator and expand the denominator. The numerator is simply 55, and the denominator is 2g(2g)−2g(3)2g(2g) - 2g(3), which simplifies to 4g2−6g4g^2 - 6g.
  4. Write Final Answer: Write the answer in the simplest form. So, the final answer is 54g2−6g\frac{5}{4g^2 - 6g}.

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