Proposition: Sum and Difference of Two Ratios

Let \(a,b,c,d\) be real numbers with \(b\neq 0\) and \(d\neq 0\). Then the sum (or difference) of the ratios $\frac ab$ and $\frac cd$ equals the ratio $\frac {ad\pm bc}{bd}$, formally $$\frac ab\pm\frac cd=\frac {ad\pm bc}{bd}.$$

Proofs: 1


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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983