Question

Further maths question
1.Express 3x-1/(x+1)(x-3) in a partial fraction
2. Simplify 2/3+5
3.Solve the quadratic equation using factorization method
a. 4x²+8x+1=0
b.3x²+4x-3=0
Maths question
1.Using a ruler and a pair of compass only construct a triangle PQR such that /QR/=6.5cm, /PQ/=3.2cm. a.construct the locus L1 of point equidistance from B and Q. Join RS and PS where S is point of intersection of L1 and L2. Measure /QS/

Answer 1

1.

$$\frac{3x-1}{(x+1)(x-3)}=\frac{A}{x+1}+\frac{B}{x-3}$$

$\frac{A}{x+1}+\frac{B}{x-3}=\frac{A(x-3)+B(x+1)}{(x+1)(x-3)}=\frac{3x-1}{(x+1)(x-3)}$

$A(x-3)+B(x+1)=3x-1$

$Ax-3A+Bx+B=3x-1$

$(A+B)x-(3A-B)=3x-1$

$\begin{alignedat}{2} A+B = 3 \\ 3A-B = 1 \end{alignedat}$ $\begin{alignedat}{2} A = 1 \\ B = 2 \end{alignedat}$

Answer

$\frac{1}{x+1}+\frac{2}{x-3}$

2. $\frac{2}{3}+5=5\frac{2}{3}=\frac{17}{3}$

3. a. $4x^{2}+8x+1=0$

$x^{2}+2x+0.25=0$

$x^{2}+2x+1-1+0.25=0$

$(x+1)^{2}-0.75=0$

$(x+1)^{2}=0.75$

$x_{1}+1=\sqrt{0.75}$ $x_{2}+1=-\sqrt{0.75}$

$x_{1}=\sqrt{0,75}-1$ $x_{2}=-\sqrt{0,75}-1$

$x_{1}=\frac{\sqrt{3}}{2}-1$ $x_{2}=-\frac{\sqrt{3}}{2}-1$

b. $3x^{2}+4x-3=0$

$x^{2}+\frac{4}{3}x-1=0$

$x^{2}+\frac{4}{3}x-1+\frac{4}{9}-\frac{4}{9}=0$

$(x+\frac{2}{3})^{2}-\frac{13}{9}=0$

$(x+\frac{2}{3})^{2}=\frac{13}{9}$

$x_{1}+\frac{2}{3}=\sqrt\frac{13}{9}$ $x_{2}+\frac{2}{3}=-\sqrt\frac{13}{9}$

$x_{1}=\frac{\sqrt{13}-2}{3}$ $x_{2}=-\frac{\sqrt{13}+2}{3}$