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]