Question

ans please ... must watch waiting for your answer​

Answer 1

Question :–

▪︎ Solve for 'x' :

$\: \: \: { \bold{2( \dfrac{2x - 1}{x + 3}) - 3( \dfrac{x + 3}{2x - 1} ) = 5 }}$ ; x ≠ -3 , ½

ANSWER :–

▪︎ x = -⅕ , x = -10

EXPLANATION :–

GIVEN :–

▪︎ $\: \: \: { \bold{2( \dfrac{2x - 1}{x + 3}) - 3( \dfrac{x + 3}{2x - 1} ) = 5}}$

TO FIND :–

Value of 'x'.

SOLUTION :–

▪︎ Let's put $\: \implies \: { \bold{\dfrac{2x - 1}{x + 3} = t}}$

$\: \\ \implies \: { \bold{2t - \frac{3}{t} = 5 }}$

$\: \\ \implies \: { \bold{2 {t}^{2} - 3 = 5 t}}$

$\: \\ \implies \: { \bold{2 {t}^{2} - 5t - 3 = 0}}$

$\: \\ \implies \: { \bold{2 {t}^{2} -6t + t - 3 = 0}}$

$\: \\ \implies \: { \bold{2 t(t - 3) +1( t - 3) = 0}}$

$\: \\ \implies \: { \bold{(2 t + 1)(t - 3) = 0}}$

$\: \\ \implies \: { \bold{t = - \dfrac{1}{2} \: , \: t = 3}}$

(1) When t = -½ :–

$\: \implies \: { \bold{\dfrac{2x - 1}{x + 3} = - \dfrac{1}{2} }}$

$\: \\ \implies \: { \bold{2(2x - 1) = - (x + 3)}}$

$\: \\ \implies \: { \bold{4x - 2 = - x - 3}}$

$\: \\ \implies \: { \bold{5x = - 1}}$

$\: \\ \implies \: { \boxed{\bold{x = - \frac{1}{5} }}}$

(2) When t = 3 :–

$\: \\ \implies \: { \bold{\dfrac{2x - 1}{x + 3} = 3}}$

$\: \\ \implies \: { \bold{2x - 1 = 3(x + 3)}}$

$\: \\ \implies \: { \bold{2x - 1 = 3x + 9}}$

$\: \\ \implies \: { \bold{2x - 3x = 1 + 9}}$

$\: \\ \implies \: { \boxed{ \bold{x= - 10}}}$