Solve

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

#### Solution

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

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

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

⇒ `{ 4x - 5}/{ 2x + 3} = 3/7`

⇒ `28x - 35 = 6x + 9`

⇒ `28x - 6x = 35 + 9`

⇒ `22x = 44`

⇒ `x = 2`

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