# How do you simplify (14r)/(9-r)-(2r)/(r-9)?

Jul 30, 2017

See a solution process below:

#### Explanation:

To subtract these fractions we need them to be over a common denominator. Because the denominators are the "opposites" of each other we can multiple one of the fractions by the form of $1$ of $- \frac{1}{-} 1$:

$\left(\frac{- 1}{-} 1 \times \frac{14 r}{9 - r}\right) - \frac{2 r}{r - 9} \implies$

$\frac{- 1 \times 14 r}{- 1 \left(9 - r\right)} - \frac{2 r}{r - 9} \implies$

$\frac{- 14 r}{- 9 + r} - \frac{2 r}{r - 9} \implies$

$\frac{- 14 r}{r - 9} - \frac{2 r}{r - 9}$

We can now subtract the numerators of the two fractions over the common denominator:

$\frac{- 14 r - 2 r}{r - 9} \implies$

$\frac{\left(- 14 - 2\right) r}{r - 9} \implies$

$\frac{- 16 r}{r - 9}$