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Simplify: (k-3)/(k)=(k+4)/(5k)-(1)/(k)

Simplify: k−3k=k+45k−1k\frac{k-3}{k}=\frac{k+4}{5k}-\frac{1}{k}

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Full solution

Q. Simplify: k−3k=k+45k−1k\frac{k-3}{k}=\frac{k+4}{5k}-\frac{1}{k}
  1. Simplify with Common Denominator: Simplify the right-hand side of the equation by finding a common denominator.\newline(k−3)/k=(k+4)/(5k)−1/k(k-3)/k = (k+4)/(5k) - 1/k\newline=(k+4−5)/(5k)= (k+4-5)/(5k)\newline=(k−1)/(5k)= (k-1)/(5k)
  2. Set Equal and Cross-Multiply: Set the simplified equation equal to the left-hand side and cross-multiply to eliminate the denominators.\newline(k−3)/k=(k−1)/(5k)(k-3)/k = (k-1)/(5k)\newlineCross-multiplying gives:\newline5k(k−3)=k(k−1)5k(k-3) = k(k-1)\newline5k2−15k=k2−k5k^2 - 15k = k^2 - k
  3. Rearrange to Quadratic Equation: Rearrange the equation to form a quadratic equation.\newline5k2−15k−k2+k=05k^2 - 15k - k^2 + k = 0\newline4k2−16k=04k^2 - 16k = 0

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