1) At what points do the graphs of \(h(x)\) and \(g(x)\) intersect if \(h\left(x\right)=\large{\frac{10-4x}{x^2-3x}}\) and \(g\left(x\right)=\large{\frac{x-7}{x-3}}\)?
2) Two positive integers differ by \(9\) and their reciprocals differ by \(\frac{1}{10}\). Find the integers.
3) Solve: \(\large{\frac{1}{x-2}=\frac{4}{x^2-4}+\frac{7}{8}}\)
4) Solve: \(\large{\frac{x}{3x-15}-\frac{7}{x^2-10x+25}=\frac{x-4}{4x-20}}\)
5) The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\), what are the integers?
6) Kate kayaks down a river and moves at a speed of \(6\) mph in still water. She rides \(99\) miles downstream in a river in the same time it would take her to travel \(33\) miles upstream. What is the speed of the current of the river?
7) Solve for y in terms of x if \( x= \frac{t}{t+1} \) and \( y = \frac{t^2}{t+1} \)
8) If \(r \) is picked at random from the set \( \{\frac{1}{4}, \frac{1}{3}, \frac{1}{2} \} \), what is the probability that \( \frac{1}{x-3} +r =0 \) has a solution less than one?
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2) Two positive integers differ by \(9\) and their reciprocals differ by \(\frac{1}{10}\). Find the integers.
3) Solve: \(\large{\frac{1}{x-2}=\frac{4}{x^2-4}+\frac{7}{8}}\)
4) Solve: \(\large{\frac{x}{3x-15}-\frac{7}{x^2-10x+25}=\frac{x-4}{4x-20}}\)
5) The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\), what are the integers?
6) Kate kayaks down a river and moves at a speed of \(6\) mph in still water. She rides \(99\) miles downstream in a river in the same time it would take her to travel \(33\) miles upstream. What is the speed of the current of the river?
7) Solve for y in terms of x if \( x= \frac{t}{t+1} \) and \( y = \frac{t^2}{t+1} \)
8) If \(r \) is picked at random from the set \( \{\frac{1}{4}, \frac{1}{3}, \frac{1}{2} \} \), what is the probability that \( \frac{1}{x-3} +r =0 \) has a solution less than one?
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