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

$$\frac { 16 x ^ { 2 } - 20 x + 9 } { 8 x ^ { 2 } + 12 x + 21 } = \frac { 4 x - 5 } { 2 x + 3 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x+3\right)\left(8x^{2}+12x+21\right), the least common multiple of 8x^{2}+12x+21,2x+3.

$$\left(2x+3\right)\left(16x^{2}-20x+9\right)=\left(8x^{2}+12x+21\right)\left(4x-5\right)$$

Use the distributive property to multiply 2x+3 by 16x^{2}-20x+9 and combine like terms.

$$32x^{3}+8x^{2}-42x+27=\left(8x^{2}+12x+21\right)\left(4x-5\right)$$

Use the distributive property to multiply 8x^{2}+12x+21 by 4x-5 and combine like terms.

$$32x^{3}+8x^{2}-42x+27=32x^{3}+8x^{2}+24x-105$$

Subtract 32x^{3} from both sides.

$$32x^{3}+8x^{2}-42x+27-32x^{3}=8x^{2}+24x-105$$

Combine 32x^{3} and -32x^{3} to get 0.

$$8x^{2}-42x+27=8x^{2}+24x-105$$

Subtract 8x^{2} from both sides.

$$8x^{2}-42x+27-8x^{2}=24x-105$$

Combine 8x^{2} and -8x^{2} to get 0.

$$-42x+27=24x-105$$

Subtract 24x from both sides.

$$-42x+27-24x=-105$$

Combine -42x and -24x to get -66x.

$$-66x+27=-105$$

Subtract 27 from both sides.

$$-66x=-105-27$$

Subtract 27 from -105 to get -132.

$$-66x=-132$$

Divide both sides by -66.

$$x=\frac{-132}{-66}$$

Divide -132 by -66 to get 2.

$$x=2$$