Question

Solve the following:

$\frac{2x-3}{2x-1}=\frac{3x-1}{3x+5}$

• A. $1\frac{2}{3}$
• B. $5\frac{2}{3}$
• C. $7\frac{2}{3}$
• D. $2\frac{2}{3}$

Answer 1

The correct option is D $2\frac{2}{3}$

$\frac{2x-3}{2x-1}=\frac{3x-1}{3x+5}$
$\Rightarrow (2x-3)(3x+5)=(2x-1)(3x-1)$
$\Rightarrow 6x^2+10x-9x-15=6x^2-2x-3x+1$
$\Rightarrow 6x=16$
$\Rightarrow x=\frac{16}{6}$
$\Rightarrow x=\frac{8}{3}$
$\Rightarrow x=2\frac{2}{3}$