How do you simplify $- \frac{2}{7 r} + \frac{4}{t}$ $-2/(7r)+4/t$ ?

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How do you simplify $- \frac{2}{7 r} + \frac{4}{t}$ $-2/(7r)+4/t$ ?

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Answer 1 · 2017-08-26T23:01:13

$= 2 {(- \frac{1}{7} r) + (\frac{2}{t})}$ $=2{(-1/7r) + (2/t)}$

Taking LCM

$= 2 {\frac{- t + 14 r}{7 r t}}$ $=2{(-t+14r)/(7rt)}$

$= \frac{2 (14 r - t)}{7 r t}$ $=(2(14r-t))/(7rt)$

Answer 2 · 2017-08-27T00:13:13

$- \frac{2}{7 r} + \frac{4}{t} = \frac{2 (14 r - t)}{7 r t}$ $-2/(7r)+4/t=color(blue)((2(14r-t))/(7rt)$

Explanation:

Simplify.

$- \frac{2}{7 r} + \frac{4}{t}$ $-2/(7r)+4/t$

Determine the least common denominator by multplying the denominators:

$7 r \times t = 7 r t$ $7rxxt=7rt$

Multiply each fraction by an equivalent fraction to make both denominators $7 r t$ $7rt$ . An equivalent fraction is one in which the numerator and denominator are the same. An equivalent fraction is equal to $1$ $1$ . For example $\frac{8}{8} = 1$ $8/8=1$ .

The expression can be rewritten as $\frac{4}{t} - \frac{2}{7 r}$ $4/t-2/(7r)$ .

$\frac{4}{t} \times \frac{7 r}{7 r} - \frac{2}{7 r} \times \frac{t}{t}$ $4/txxcolor(magenta)((7r)/(7r))-(2)/(7r)xxcolor(teal)(t/t$

Simplify.

$\frac{28 r}{7 r t} - \frac{2 t}{7 r t}$ $(28r)/(7rt)-(2t)/(7rt)$

Combine the numerators.

$\frac{28 r - 2 t}{7 r t}$ $(28r-2t)/(7rt)$

Simplify the numerator by factoring out the common $2$ $2$ .

$\frac{2 (14 r - t)}{7 r t}$ $(2(14r-t))/(7rt)$

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2 Answers

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