Question

Solve the following quadratic equation by factorization, the roots are :$-1$, $-5$
$\frac{x+3}{x+2}=\frac{3x-7}{2x-3}$

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{x+3}{x+2}=\frac{3x-7}{2x-3}$

$\Rightarrow$ $(x+3)(2x-3)=(3x-7)(x+2)$

$\Rightarrow$ $2x^2-3x+6x-9=3x^2+6x-7x-14$

$\Rightarrow$ $3x^2+6x-7x-14-2x^2+3x-6x+9=0$

$\Rightarrow$ $x^2-4x-5=0$

$\Rightarrow$ $x^2-5x+1x-5=0$

$\Rightarrow$ $x(x-5)+1(x-5)=0$

$\Rightarrow$ $(x-5)(x+1)=0$

$\Rightarrow$ $x-5=0$ and $x+1=0$

$\Rightarrow$ $x=5$ and $x=-1$

$\therefore$ We can see $-1,5$ are not roots of the given quadratic equation.

$\therefore$ The given statement is false.