Question

Solve the following equations.
$\frac{x^2-3.5x+1.5}{x^2-x-6}=0$

Answer 1

$\frac{x^2-3.5x+1.5}{x^2-x-6}=0$

$10x^2-35x+15=0$

$2x^2-7x+3=0$

$2x^2-x-6x+3=0$

$x(2x-1)-3(2x-1)=0$

$(2x-1)(x-3)=0$

$(2x-1)=0$ $(x-3)=0$

$x$=$\frac{1}{2}$and $x=3$

but $x^2-x-6\ne 0$

$x^2-3x+2x-6\ne 0$

$x(x-3)+2(x-3)\ne 0$

$(x-3)(x+2)\ne 0$

$x\ne 3$ and $x\ne -2$