Solve 168329.461div76260 | Microsoft Math Solver

Evaluate

\frac{168329461}{76260000}\approx 2.207310005

Solution Steps

168329.461 \div 76260

Expand \frac{168329.461}{76260} by multiplying both numerator and the denominator by 1000.

\frac{168329461}{76260000}

Factor

\frac{17 \cdot 1319 \cdot 7507}{3 \cdot 31 \cdot 41 \cdot 2 ^ {5} \cdot 5 ^ {4}} = 2\frac{15809461}{76260000} = 2.2073100052452137

Quiz

Arithmetic

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168329.461 \div 76260

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Find this Determinant

https://math.stackexchange.com/questions/1349619/find-this-determinant

I guess it's easier to go for a reduction formula. I proceed along the generalization mentioned in comment : Call the determinant M = M_n(x_1,x_2,\cdots, x_n) \displaystyle \begin{align}M &= \left|\begin{matrix}\dfrac{1}{x_1+x_1} & \cdots & \dfrac{1}{x_1+x_n}\\ \dfrac{1}{x_2+x_1} & \cdots & \dfrac{1}{x_2+x_n}\\ \cdot & \cdot &\cdot \\ \dfrac{1}{x_n+x_1} & \cdots & \dfrac{1}{x_n+x_n}\end{matrix}\right| \\& \text{subtract R1 from each row} \\&= \left|\begin{matrix}\dfrac{1}{x_1+x_1} & \cdots & \dfrac{1}{x_1+x_n}\\ \dfrac{x_1 - x_2}{(x_2+x_1)(x_1+x_1)} & \cdots & \dfrac{x_1 - x_2}{(x_2+x_n)(x_1+x_n)}\\ \cdot & \cdot &\cdot \\ \dfrac{x_1 - x_n}{(x_n+x_1)(x_1+x_1)} & \cdots & \dfrac{x_1 - x_n}{(x_n+x_n)(x_1+x_n)}\end{matrix}\right| \\&= \prod\limits_{j=2}^{n} (x_1 - x_j)\times \prod\limits_{j=1}^{n}\frac{1}{(x_1+x_j)} \times \left|\begin{matrix}1 & \cdots & 1\\ \dfrac{1}{(x_2+x_1)} & \cdots & \dfrac{1}{(x_2+x_n)}\\ \cdot & \cdot &\cdot \\ \dfrac{1}{(x_n+x_1)} & \cdots & \dfrac{1}{(x_n+x_n)}\end{matrix}\right|\end{align} ...

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\frac{168329461}{76260000}

Expand \frac{168329.461}{76260} by multiplying both numerator and the denominator by 1000.

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