4.1 Homework 26.11.14

To be done in the front of your books neatly for Tue 2nd Dec. 24 Marks

1. Simplify
   1. \[\frac{3}{x-3}-\frac{4}{(x-3)^2}\]
   2. \[\frac{3}{x-2}+\frac{2}{x+5}\]

   [6 marks]

2. Simplify \[\frac{3x}{4x^2-25}-\frac{2}{2x^2-3x-5}\]

   [4 marks]

3. Solve, giving answers to 3 significant figures \[ \sqrt{ \frac{(\sqrt{x}+3)^2-5}{3} -3} = 6 \]

   [4 marks]

4. Solve \[ \begin{align*} 5&x+4y=-49 \\ -3&x+8y=45 \end{align*} \]

   [3 marks]

5. Solve, showing the solution on a number line \[ -3<\frac{2x-5}{3}\leq5 \]

   [3 marks]

6. Shade the region which satisfies these inequalities on a pair of x,y axes: \[ -3 < x \leq 2 \\ -4 \leq y < 5 \\ x+y > 1 \]

   [4 marks]