Rational Expressions Problem Set 1

If \(\frac{2}{x-5}+\frac{3}{x-5}=\frac{n}{x-5}\), what is the value of \(n\)?

\[\frac{1}{r-7}+\frac{r+2}{r-7}=6\]

In the equation above, if \(r\neq 7\), what is the value of \(r\)?

\[\frac{m}{2m+8}+\frac{2}{m+4}=3\]

In the equation above, what is the value of \(m\)?

\[\frac{2x+2}{(x+5)(x-3)}-\frac{x-3}{(x+5)(x-3)}=1\]

In the equation above, if \(x\) is a positive integer \(x\neq 3\), what is the value of \(x\)?