# How do you combine c/(7-c)+(2c-7)/(c-7)?

Aug 23, 2016

$1$

#### Explanation:

There is a very useful way of changing the signs of an expression around.

"Multiplying by a negative, changes the signs"

$- \left(x - y\right) = \left(- x + y\right) = \left(y - x\right)$

OR: $\left(2 p - q\right) = - \left(q - 2 p\right) \text{ }$Notice the "switch-rounds"

We can apply this in the second fraction to make the denominators the same:

$\frac{c}{\left(7 - c\right)} \textcolor{red}{-} \frac{2 c - 7}{\textcolor{red}{\left(7 - c\right)}} \text{ "rArr " same denominators}$

=$\frac{c \textcolor{b l u e}{-} \left(2 c - 7\right)}{7 - c} \text{ notice the multiplying by a negative}$

$\frac{c - 2 c + 7}{7 - c}$

=color(teal)(-c+7)/(7-c) = color(teal)(7-c)/(7-c) " " color(teal)(" by the commutative law")

$\frac{\cancel{7 - c}}{\cancel{7 - c}} = 1$