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August 29th, 2016, 11:32 AM   #1
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Simplifying fractions

Hi, can someone take a look at this please to see if I have it correct? Many thanks.

I've been asked to express the following as a single fraction

$\frac{1}{T1}+\frac{1}{T2}+\frac{1}{T3}$

have I done this correct to

= $\frac{T2T3+T1T3+T1T2}{T1T2T3}$

Last edited by skipjack; October 12th, 2016 at 05:14 AM.
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August 29th, 2016, 11:35 AM   #2
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this is correct as you can see by doing the division for each term.
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October 12th, 2016, 03:45 AM   #3
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Since we are adding fractions with a different denominator , therefore we need to find equivalent fraction of each fraction . Equivalent fractions should have a common denominator.

Greatest common divisor = T1T2T3
1/T1 = T2T3/T1T2T3
1/T2 = T1T3/T1T2T3
1/T3 = T1T2/T1T2T3

Now, add the fractions
1/T1 + 1/T2 + 1/T3 = (T2T3 + T1T3 + T1T2)/T1T2T3
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October 12th, 2016, 08:23 AM   #4
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Quote:
Originally Posted by rahuljoshi View Post
Since we are adding fractions with a different denominator , therefore we need to find equivalent fraction of each fraction . Equivalent fractions should have a common denominator.

Greatest common divisor = T1T2T3
1/T1 = T2T3/T1T2T3
1/T2 = T1T3/T1T2T3
1/T3 = T1T2/T1T2T3

Now, add the fractions
1/T1 + 1/T2 + 1/T3 = (T2T3 + T1T3 + T1T2)/T1T2T3
You need grouping symbols around those products in those denominators when they are typed out horizontally.
Also, it would be clearer to use an asterisk to separate all of your variables, because the subscripts start looking
like coefficients, as your similar-looking variables are all mashed together.

At a minimum:

Greatest common divisor = T1T2T3
1/T1 = T2T3/(T1T2T3)
1/T2 = T1T3/(T1T2T3)
1/T3 = T1T2/(T1T2T3)

Now, add the fractions
1/T1 + 1/T2 + 1/T3 = (T2T3 + T1T3 + T1T2)/(T1T2T3)

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More clarity:

Greatest common divisor = T1*T2*T3
1/T1 = T2*T3/(T1*T2*T3)
1/T2 = T1*T3/(T1*T2*T3)
1/T3 = T1*T2/(T1*T2*T3)

Now, add the fractions
1/T1 + 1/T2 + 1/T3 = (T2*T3 + T1*T3 + T1*T2)/(T1*T2*T3)
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