Question

Solve the quadratic equation
By factorization or general
formula method.
4/x -3=5/2x+3​

Answer 1

$\sf\huge {\underline{\underline{{Solution}}}}$

$\sf \implies \dfrac{4}{x - 3} = \dfrac{5}{2x + 3}$

We see that on both sides fractional values Now, cross multiply to both sides

$\sf \implies4(2x + 3 ) = 5(x - 3)$

Now, opening the brackets and expanding the terms.

$\sf \implies8x + 12 = 5x - 15$

Shifts Variable to one side and make constant to another side.

$\sf \implies8x - 5x = - 15 - 12$

$\sf \implies3x = - 27$

$\sf \implies \: x = - \dfrac{ 27}{3} = - 9$

∴ x= -9

Check:

$\sf \implies \dfrac{4}{x - 3} = \dfrac{5}{2x + 3}$

Solving LHS

$\sf \implies\dfrac{4}{ - 9 - 3} = \dfrac{4}{ - 12} = - \dfrac{1}{3}$

solving RHS

$\sf \implies \dfrac{5}{2( - 9) + 3} = \dfrac{5}{ - 18 + 3} = \dfrac{5}{ - 15} = -\dfrac{1}{3}$

Since,LHS = RHS ( Verified)