$\dfrac{a+b}{a-b}$. the particular expression in my case is:
$$ \frac{20 \sin(x)-1}{20 \sin(x)+1} $$
the value of $\sin x$ is $\dfrac{100}{\sqrt{1000^2-100^2}}$ so it's very hard to do it by simple arithmetic.
What is the general method for easily solving these type of expressions? $(a+b)/(a-b)$
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arithmetic
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1$\sqrt{1000^2-100^2}=\sqrt{100^2(10^2-1)}=100\sqrt{99}=300\sqrt{11}$ so in the end $\sin(x)=\cfrac{1}{3\sqrt{11}}$ which is no longer so very hard to work with directly. – 2017-02-11
1 Answers
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Generally we have that $$\frac{a-b}{a+b}=\frac{a+b}{a-b}\frac{a-b}{a-b}=\frac{a^2-b^2}{(a+b)^2}$$ and that $$\frac{a+b}{a-b}=\left(\frac{a-b}{a+b}\right)^{-1}=\frac{(a+b)^2}{a^2-b^2}$$