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(m-4)/(3m-3)-(4m)/(2m-4)

m−43m−3−4m2m−4 \frac{m-4}{3 m-3}-\frac{4 m}{2 m-4}

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Full solution

Q. m−43m−3−4m2m−4 \frac{m-4}{3 m-3}-\frac{4 m}{2 m-4}
  1. Factor Common Denominators: First, factor out the common terms in the denominators.\newline(3m−3)(3m-3) can be factored as 3(m−1)3(m-1).\newline(2m−4)(2m-4) can be factored as 2(m−2)2(m-2).
  2. Rewrite with Factored Denominators: Now rewrite the expression with the factored denominators. m−43(m−1)−4m2(m−2)\frac{m-4}{3(m-1)} - \frac{4m}{2(m-2)}
  3. Find Common Denominator: Find a common denominator to combine the fractions.\newlineThe common denominator is 3×2×(m−1)×(m−2)=6(m−1)(m−2)3\times 2\times (m-1)\times (m-2) = 6(m-1)(m-2).
  4. Rewrite with Common Denominator: Rewrite each fraction with the common denominator. (m−4)⋅2⋅(m−2)6(m−1)(m−2)−(4m)⋅3⋅(m−1)6(m−1)(m−2)\frac{(m-4)\cdot 2 \cdot (m-2)}{6(m-1)(m-2)} - \frac{(4m)\cdot 3 \cdot (m-1)}{6(m-1)(m-2)}
  5. Expand Numerators: Expand the numerators. 2m(m−2)−8(m−2)6(m−1)(m−2)−12m(m−1)6(m−1)(m−2)\frac{2m(m-2) - 8(m-2)}{6(m-1)(m-2)} - \frac{12m(m-1)}{6(m-1)(m-2)}
  6. Simplify Numerators: Simplify the expanded numerators. [2m2−4m−8m+16−12m2+12m]/[6(m−1)(m−2)][2m^2 - 4m - 8m + 16 - 12m^2 + 12m]/[6(m-1)(m-2)]
  7. Combine Like Terms: Combine like terms in the numerator.\newline(−10m2+4m+16)/[6(m−1)(m−2)](-10m^2 + 4m + 16)/[6(m-1)(m-2)]
  8. Cancel Common Factors: Now, simplify the expression by canceling out common factors if possible. There are no common factors to cancel out in this case.
  9. Final Simplification: The expression is now simplified. −10m2+4m+166(m−1)(m−2)\frac{-10m^2 + 4m + 16}{6(m-1)(m-2)}

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