Question

drag the tiles to the correct boxes to complete the pairs. match each rational expression to its simplest form. \\(\frac{2m^2 - 4m}{2(m - 2)}\\) \\(\frac{m^2 - 2m + 1}{m - 1}\\) \\(\frac{m^2 - 3m + 2}{m^2 - m}\\) \\(\frac{m^2 - m - 2}{m^2 - 1}\\) \\(\frac{m - 2}{m}\\) \\(m - 1\\) \\(\frac{m - 2}{m - 1}\\) \\(m\\)

Explanation:

Step1: Simplify \(\frac{2m^2 - 4m}{2(m - 2)}\)

Factor numerator: \(2m(m - 2)\). Then \(\frac{2m(m - 2)}{2(m - 2)} = m\) (cancel \(2(m - 2)\)).

Step2: Simplify \(\frac{m^2 - 2m + 1}{m - 1}\)

Factor numerator: \((m - 1)^2\). Then \(\frac{(m - 1)^2}{m - 1}=m - 1\) (cancel \(m - 1\)).

Step3: Simplify \(\frac{m^2 - 3m + 2}{m^2 - m}\)

Factor numerator: \((m - 1)(m - 2)\), denominator: \(m(m - 1)\). Cancel \(m - 1\): \(\frac{m - 2}{m}\).

Step4: Simplify \(\frac{m^2 - m - 2}{m^2 - 1}\)

Factor numerator: \((m - 2)(m + 1)\), denominator: \((m - 1)(m + 1)\). Cancel \(m + 1\): \(\frac{m - 2}{m - 1}\).

Answer:

• \(\frac{m - 2}{m}\) ↔ \(\frac{m^2 - 3m + 2}{m^2 - m}\)
• \(m - 1\) ↔ \(\frac{m^2 - 2m + 1}{m - 1}\)
• \(\frac{m - 2}{m - 1}\) ↔ \(\frac{m^2 - m - 2}{m^2 - 1}\)
• \(m\) ↔ \(\frac{2m^2 - 4m}{2(m - 2)}\)