Question

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

Answer 1

`1`

Explanation:

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

"Multiplying by a negative, changes the signs"

`- (x-y) = (-x+y)= (y-x)`

OR: `(2p - q) = -(q-2p)" "`Notice the "switch-rounds"

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

`c/((7-c))color(red)(-)(2c-7)/color(red)((7-c)) " "rArr " same denominators"`

=`(c color(blue)(-)(2c-7))/(7-c) " notice the multiplying by a negative"`

`(c -2c+7)/(7-c)`

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

`(cancel(7-c))/(cancel(7-c)) = 1`