Question

Rewrite the quadratic equation $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30},x\ne -4,7$
in the standard form of a quadratic equation. Also,identify a,b and c in the given equation.

Answer 1

$\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}$
$\Rightarrow \frac{x-7-x-4}{(x+4)(x-7)}=\frac{11}{30}$
$\Rightarrow -\frac{11}{(x+4)(x-7)}=\frac{11}{30}$
$\Rightarrow (x+4)(x-7)=-30$
$\Rightarrow x^2-3x-28=-30$
$\Rightarrow x^2-3x+2=0$
On comparing this equation with $a{x}^2+bx+c=0$, we get
a = 1, b = -3 and c = 2