Question

solve for x 6x² + 13x-4 / 2x+5 =
12x² + 5x -2 / 4x +3​

Answer 1

ANSWER = 1

$\frac{( 6 {x}^{2} + 13x - 4) }{(2x + 5)} \: \: \: = \: \: \frac{(12 {x}^{2} + 5x - 2)}{(4x + 3)}$

LHS

$\Rightarrow \: (6{x}^{2} + 13x -4) \times (4x+3)$

$\Rightarrow \: 24 {x}^{3} + 18 {x}^{2} + 52 {x}^{2} + 39x - 16x - 12$

$\Rightarrow \: \: 24 {x}^{3} + 70 {x}^{2} + 23x - 12$

RHS

$\Rightarrow \: \: (12 {x}^{2} + 5x - 2) \times (2x + 5)$

$\Rightarrow \: \: 24 {x}^{ 3} + 60 {x}^{2} + 10 {x}^{2} + 25x - 4x - 10$

$\Rightarrow \: 24 {x}^{3} + 70 {x}^{2} + 21x - 10$

SINCE LHS =RHS

==> 24x³ + 70x² + 23x - 12 = 24x³ +70 x² +21x -10

==> 24x³ - 24x³ + 70x² -70 x² + 23 x - 21 x = 12 - 10

==> 24x³ - 24x³ + 70x² -70 x² + 23 x - 21 x = 12 - 10

$23x - 21x \: = 12 - 10$

$2x \: \: = \: 2$

$x \: = 1$