Thread: Manipulating Fractions
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Old November 15th, 2008, 01:52 PM
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{\color{red}\frac{4}{3 + \displaystyle \frac{10t}{(1+t^2)}}} \ \cdot \ {\color{blue}\frac{2}{1+t^2}}

To multiply fractions, simply multiply numerator by numerator and denominator by denominator:

= \frac{{\color{red}4} \cdot {\color{blue}2}}{{\color{red}\left(3 + \displaystyle \frac{10t}{(1+t^2)}\right)}{\color{blue}\left(1+t^2\right)}}

You should know that: a(b+c) = ab + ac. Here, imagine a = {\color{blue}1+t^2}.

So, simplifying:
= \frac{8}{{\color{red}3}{\color{blue}(1+t^2)} + \displaystyle \frac{{\color{red}10t}}{{\color{blue}1+t^2}} {\color{blue}\left(1+t^2\right)}}

Notice that in the denominator, the 1 + t^2 cancels out in the second term, so we get:

= \frac{8}{3(1+t^2) + 10t}

and so on and so on ..
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