Question

find the root of following quadratic equations x+3/x+2=3x-7/2x-3​

Answer 1

${\red{\text{Roots are }5 \:\:or\:\:-1}}$

${\large{\underline{\text{Given :}}}}$

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

${\large{\underline{\text{Solution :}}}}$

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

${\red{\text{Cross multiply the terms}}}$

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

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

$\implies 2x^2+3x-9 = 3x^2-x-14$

${\red{\text{Bring all terms to LHS side}}}$

$\implies 3x^2-2x^2-x-3x-14+9 = 0$

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

${\red{\text{Solve out the quadratic equation }}}$

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

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

$\implies (x-5)(x+1)$

$\implies x=5(or) -1$