# How do you simplify -2/(7r)+4/t?

Aug 26, 2017

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

Taking LCM

$= 2 \left\{\frac{- t + 14 r}{7 r t}\right\}$

$= \frac{2 \left(14 r - t\right)}{7 r t}$

Aug 27, 2017

-2/(7r)+4/t=color(blue)((2(14r-t))/(7rt)

#### Explanation:

Simplify.

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

Determine the least common denominator by multplying the denominators:

$7 r \times t = 7 r t$

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

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

4/txxcolor(magenta)((7r)/(7r))-(2)/(7r)xxcolor(teal)(t/t

Simplify.

$\frac{28 r}{7 r t} - \frac{2 t}{7 r t}$

Combine the numerators.

$\frac{28 r - 2 t}{7 r t}$

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

$\frac{2 \left(14 r - t\right)}{7 r t}$