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

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

"Multiplying by a negative, changes the signs"

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

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

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To combine the given expression, c/(7-c) + (2c-7)/(c-7), we need to find a common denominator and then add the fractions together. The common denominator is (7-c)(c-7).

Multiplying the first fraction by (c-7)/(c-7) and the second fraction by (7-c)/(7-c), we get:

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

Expanding and simplifying the numerators, we have:

(c^2 - 7c + 14c - 7)/((7-c)(c-7))

Combining like terms in the numerator, we get:

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

Therefore, the combined expression is (c^2 + 7c - 7)/((7-c)(c-7)).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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