Algebra

$\frac{1}{1 \cdot 4} + \frac{1}{7 \cdot 10} + \frac{1}{37 + 40}\\ =\frac{1}{1 \cdot 2^2} + \frac{1}{7 \cdot 2\cdot 5} + \frac{1}{7\cdot 11}\\ =\frac{5\cdot7\cdot 11+2\cdot 11+2^2\cdot 5}{2^2\cdot 5\cdot7\cdot 11}\\ =\frac{427}{2^2\cdot 5\cdot7\cdot 11}\\ =\frac{7\cdot 61}{2^2\cdot 5\cdot7\cdot 11}\\ \color{blue}=\frac{61}{2^2\cdot 5\cdot 11}$

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1/4+1/70+1/77

1/70+1/77=21/770=3/110

3/110+1/4 = 61/220

correct me if i'm wrong!