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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

#1
+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
+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 .

$$=\,\frac{1}{6x}$$

hectictar Mar 15, 2018