Question

Find $x$ by solving the given equation:

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

• A. $5,-1$
• B. $-5,-1$
• C. $5,1$
• D. $-5,1$

Answer 1

Answer: (A)

$5,-1$

Given,

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

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

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

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

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

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

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

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

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