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

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Answer 1 · 2016-08-23T13:32:01

$1$

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:

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

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

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

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

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

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