Algebra 1

a) Your friend's mistake is claiming that $x-3$ and $3-x$ are common factors. In fact, they are not. Imagine plugging in 4 for x. $x-3 = 4-3 = 1$. However, $3-x = 3-4 = -1$, showing that these are not equivalent expressions. b) You can factor out a negative from our second term: $\frac{x}{3-x}$, making it $-\frac{x}{x - 3}$. Now we have the common term $x-3$ that can cancel.
a) Your friend's mistake is claiming that $x-3$ and $3-x$ are common factors. In fact, they are not. Imagine plugging in 4 for x. $x-3 = 4-3 = 1$. However, $3-x = 3-4 = -1$, showing that these are not equivalent expressions. b) You can factor out a negative from our second term: $\frac{x}{3-x}$, making it $-\frac{x}{x - 3}$. Now we have the common term $x-3$ that can cancel.