Question

The value of 'x' in (x+3)/(8x+9)= x/(3x+4) is 2. But how?

Answer 1

(x+3)/(8x+9) = x/(3x+4)

(x+3) (3x+4) = x (8x+9)

3x² + 4x + 9x + 12 = 8x² + 9x

3x² + 13x + 12 = 8x² + 9x

8x² - 3x² = 13x - 9x + 12

5x² = 4x + 12

5x² - 4x - 12 = 0

5x² -10x + 6x - 12 = 0

5x(x - 2) + 6(x - 2) = 0

(x - 2) (5x + 6) = 0

=> x - 2 = 0

=> x = +2

Hope it helps...!

Thanks :)

Answer 2

(x + 3)/(8x + 9) = x/(3x + 4)

(cross multiply)

=> (x + 3)(3x + 4) = x(8x + 9)

=> 3x^2 + 9x + 4x + 12 = 8x^2 + 9x

=> 4x - 5x^2  = -12

substituting x for 2;

LHS: 4 x 2 - 5 x 2 x 2

= 8 - 20 = -12 = RHS

hence proved