checking?

[Handicap Joe]

Subtract and simplify if possible
(6-z)/(z-4) - (5z-7)/(4-z)
(6-z+(-5z)+7)/(z-4+4-z)
-6z+13
How'd I do on this one?

 

[Loren]

I didn't get that. In order to add or subtract fractions, they must have the same denominator. There are different ways to achieve this. As I see it, the simplest way would be to multiply both terms of the second fraction by -1. That gives you both fractions having the same denominator. Then combine the numerators following the rules of subtraction and place that over the common denominator.

 

[hongsgirl]

Hi Handicap Joe

Subtract and simplify if possible
(6-z)/(z-4) - (5z-7)/(4-z)
(6-z+(-5z)+7)/(z-4+4-z)
-6z+13
How'd I do on this one?

No, that's not right.

\(\displaystyle \frac{6-z}{z-4}-\frac{5z-7}{4-z}\neq \frac{6-z-5z+7}{z-4+4-z}\)

For fraction, you can't just add or subtract the numerator and denominator. Simple example :

\(\displaystyle \frac{1}{2}+\frac{1}{2}=\frac{1+1}{2}=\frac{2}{2}=1\, \text{, not}\, \frac{1}{2}+\frac{1}{2}=\frac{1+1}{2+2}=\frac{2}{4}\longrightarrow \text{wrong}\)


So, to add or subtract fraction, the denominator must be the same, and we just subtract or add the numerator.

\(\displaystyle \frac{6-z}{z-4}-\frac{5z-7}{4-z}\)

\(\displaystyle =\frac{6-z}{z-4}*\frac{4-z}{4-z}-\frac{5z-7}{4-z}*\frac{z-4}{z-4}\)

\(\displaystyle =\frac{(6-z)(4-z)}{(z-4)(4-z)}-\frac{(5z-7)(z-4)}{(4-z)(z-4)}}\)

\(\displaystyle =\frac{(6-z)(4-z)-(5z-7)(z-4)}{(z-4)(4-z)}\)

Can you continue?

 

[Loren]

Let's not make it difficult.
\(\displaystyle \frac{6-z}{z-4}-\frac{5z-7}{4-z}=\frac{6-z}{z-4}+\frac{5z-7}{z-4}=\frac{(6-z)+(5z-7)}{z-4}=\) you take it from there.

 

[Handicap Joe]

okay here it is:

(6-z+5z-7)/(z-4) = (4z-1)/(z-4)

how'd I do?

 

[mmm4444bot]

Your result is correct.