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adding and subtracting algebraic fractions  - write as a single fraction in its simplest form 

a) 3x/4 - x/8

b) 3x/4 - x/3

c)4/15x - 3/30x

 Mar 14, 2018

Best Answer 

 #1
avatar+7612 
+2

a)  \(\frac{3x}{4}-\frac{x}{8}\)

                             Multiply the first fraction by  \(\frac22\)

\(=\,\frac22\cdot\frac{3x}{4}-\frac{x}{8}\\~\\ =\,\frac{6x}{8}-\frac{x}{8}\)

                             Now that we have a commond denominator we can combine the terms.

\(=\,\frac{6x-x}{8}\\~\\ =\,\frac{5x}{8}\)

 

 

b)  \(\frac{3x}{4}-\frac{x}{3}\)

                                   Multiply the first fraction by \(\frac33\)  and the second fraction by  \(\frac44\)

\(=\,\frac33\cdot\frac{3x}{4}-\frac{x}{3}\cdot\frac44\\~\\ =\,\frac{9x}{12}-\frac{4x}{12}\\~\\ =\,\frac{9x-4x}{12}\\~\\ =\,\frac{5x}{12}\)

 

 

c)  Technically what you've written is  \(\frac{4}{15}x-\frac{3}{30}x\)    but I will do  \(\frac{4}{15x}-\frac{3}{30x}\)

 

\(\frac{4}{15x}-\frac{3}{30x}\)

                                  Multiply the first fraction by  \(\frac22\)

\(=\,\frac22\cdot\frac{4}{15x}-\frac{3}{30x} \\~\\ =\,\frac{8}{30x}-\frac{3}{30x}\\~\\ =\,\frac{8-3}{30x}\\~\\ =\,\frac{5}{30x}\)

                                  Now we can reduce this fraction by  5 .

\(=\,\frac{1}{6x}\)

.
 Mar 15, 2018
 #1
avatar+7612 
+2
Best Answer

a)  \(\frac{3x}{4}-\frac{x}{8}\)

                             Multiply the first fraction by  \(\frac22\)

\(=\,\frac22\cdot\frac{3x}{4}-\frac{x}{8}\\~\\ =\,\frac{6x}{8}-\frac{x}{8}\)

                             Now that we have a commond denominator we can combine the terms.

\(=\,\frac{6x-x}{8}\\~\\ =\,\frac{5x}{8}\)

 

 

b)  \(\frac{3x}{4}-\frac{x}{3}\)

                                   Multiply the first fraction by \(\frac33\)  and the second fraction by  \(\frac44\)

\(=\,\frac33\cdot\frac{3x}{4}-\frac{x}{3}\cdot\frac44\\~\\ =\,\frac{9x}{12}-\frac{4x}{12}\\~\\ =\,\frac{9x-4x}{12}\\~\\ =\,\frac{5x}{12}\)

 

 

c)  Technically what you've written is  \(\frac{4}{15}x-\frac{3}{30}x\)    but I will do  \(\frac{4}{15x}-\frac{3}{30x}\)

 

\(\frac{4}{15x}-\frac{3}{30x}\)

                                  Multiply the first fraction by  \(\frac22\)

\(=\,\frac22\cdot\frac{4}{15x}-\frac{3}{30x} \\~\\ =\,\frac{8}{30x}-\frac{3}{30x}\\~\\ =\,\frac{8-3}{30x}\\~\\ =\,\frac{5}{30x}\)

                                  Now we can reduce this fraction by  5 .

\(=\,\frac{1}{6x}\)

hectictar Mar 15, 2018

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