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

Simplify with Common Denominator: Simplify the right-hand side of the equation by finding a common denominator. (k-3)/k = (k+4)/(5k) - 1/k = (k+4-5)/(5k) = (k-1)/(5k) Set Equal and Cross-Multiply: Set the simplified equation equal to the left-hand side and cross-multiply to eliminate the denominators. (k-3)/k = (k-1)/(5k) Cross-multiplying gives: 5k(k-3) = k(k-1) 5k^2 - 15k = k^2 - k Rearrange to Quadratic Equation: Rearrange the equation to form a quadratic equation. 5k^2 - 15k - k^2 + k = 0 4k^2 - 16k = 0

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

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Algebra 2

Sum of finite series starts from 1

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Q. Simplify:

\frac{k-3}{k}=\frac{k+4}{5k}-\frac{1}{k}

Simplify with Common Denominator: Simplify the right-hand side of the equation by finding a common denominator. $\newline$ $(k-3)/k = (k+4)/(5k) - 1/k$ $\newline$ $= (k+4-5)/(5k)$ $\newline$ $= (k-1)/(5k)$
Set Equal and Cross-Multiply: Set the simplified equation equal to the left-hand side and cross-multiply to eliminate the denominators. $\newline$ $(k-3)/k = (k-1)/(5k)$ $\newline$ Cross-multiplying gives: $\newline$ $5k(k-3) = k(k-1)$ $\newline$ $5k^2 - 15k = k^2 - k$
Rearrange to Quadratic Equation: Rearrange the equation to form a quadratic equation. $\newline$ $5k^2 - 15k - k^2 + k = 0$ $\newline$ $4k^2 - 16k = 0$