Question

Find the roots of the following equations:
ii) $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30},x\ne -4,7$.

Answer 1

(i) $x-\frac{1}{x}=3,x\ne 0$

$\Rightarrow x^2-3x-1=0$

$\Rightarrow x=\frac{3\pm \sqrt{9+4}}{2}$

$\Rightarrow x=\frac{3+\sqrt{1}3}{2},\frac{3-\sqrt{1}3}{2}$

(ii)$\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30},x\ne -4,7$

$\Rightarrow 30x-210-30x-120=11x^2-33x-840$

$\Rightarrow 11x^2-33x-510=0$

$\Rightarrow x=\frac{33\pm \sqrt{(33{)}^2+4(11\left)\right(510)}}{2\left(11\right)}$

$\Rightarrow x=\frac{33\pm \sqrt{2}3529}{2\left(11\right)}$

$\Rightarrow x=\frac{3}{2}\pm \sqrt{\frac{2139}{44}}$