Question

Solve. 

`[ 16x^2 - 20x +9]/[ 8x^2 + 12x + 21] = ( 4x - 5 )/( 2x + 3)`

Answer 1

`[ 16x^2 - 20x +9]/[ 8x^2 + 12x + 21] = ( 4x - 5 )/( 2x + 3)`

If x = 0, then

`[ 16 xx 0 - 20 xx 0 + 9]/[ 8 xx 0 + 21 xx 0 + 21] =  [ 4 xx 0 - 5]/[ 2 xx 0 + 3] ⇒ 9/21 = -5/3`, which is not true.

So, x = 0 is not a solution of the given equation.

Now,

⇒ `[ 16x^2 - 20x + 9]/[ 8x^2 + 12x +21] = [ 4x - 5]/[2x + 3]`

`= [(16x^2 - 20x + 9) -4x( 4x - 5)]/[(8x^2 + 12x +21) - 4x( 2x + 3 )`   ...( Theorem of equal ratios)

`= [16x^2 - 20x + 9- (16x^2 - 20x)]/[8x^2 + 12x +21 - (8x^2 + 12x)]`

`= [16x^2 - 20x + 9- 16x^2 + 20x]/[8x^2 + 12x +21 - 8x^2 - 12x]`

`= [cancel(16x^2) - cancel(20x) + 9 - cancel(16x^2) + cancel(20x)]/[cancel(8x^2) + cancel(12x) + 21 - cancel(8x^2) - cancel(12x)]`

⇒ `9/ 21`

`therefore { 4x - 5}/{ 2x + 3} = 9/21`

⇒ `{4x - 5}/{2x + 3} = 3/7`

⇒ 7(4x - 5) = 3(2x + 3)

⇒ 28x - 35 = 6x + 9

⇒ 28x - 6x = 35 + 9

⇒ 22x = 44

⇒ x = 2

Thus, the solution of the given equation is x = 2.