Solve 2(x+2)(x-6)/3(x-3)(x-2)

$$\frac { 2 ( x + 2 ) ( x - 6 ) } { 3 ( x - 3 ) ( x - 2 ) }$$

Evaluate

$$\frac{2\left(x-6\right)\left(x+2\right)}{3\left(x-3\right)\left(x-2\right)}$$

Short Solution Steps

Use the distributive property to multiply 2 by x+2.

$$\frac{\left(2x+4\right)\left(x-6\right)}{3\left(x-3\right)\left(x-2\right)}$$

Apply the distributive property by multiplying each term of 2x+4 by each term of x-6.

$$\frac{2x^{2}-12x+4x-24}{3\left(x-3\right)\left(x-2\right)}$$

Combine -12x and 4x to get -8x.

$$\frac{2x^{2}-8x-24}{3\left(x-3\right)\left(x-2\right)}$$

Use the distributive property to multiply 3 by x-3.

$$\frac{2x^{2}-8x-24}{\left(3x-9\right)\left(x-2\right)}$$

Apply the distributive property by multiplying each term of 3x-9 by each term of x-2.

$$\frac{2x^{2}-8x-24}{3x^{2}-6x-9x+18}$$

Combine -6x and -9x to get -15x.

$$\frac{2x^{2}-8x-24}{3x^{2}-15x+18}$$

Expand

$$\frac{2\left(x^{2}-4x-12\right)}{3\left(x-3\right)\left(x-2\right)}$$

Short Solution Steps

Use the distributive property to multiply 2 by x+2.

$$\frac{\left(2x+4\right)\left(x-6\right)}{3\left(x-3\right)\left(x-2\right)}$$

Apply the distributive property by multiplying each term of 2x+4 by each term of x-6.

$$\frac{2x^{2}-12x+4x-24}{3\left(x-3\right)\left(x-2\right)}$$

Combine -12x and 4x to get -8x.

$$\frac{2x^{2}-8x-24}{3\left(x-3\right)\left(x-2\right)}$$

Use the distributive property to multiply 3 by x-3.

$$\frac{2x^{2}-8x-24}{\left(3x-9\right)\left(x-2\right)}$$

Apply the distributive property by multiplying each term of 3x-9 by each term of x-2.

$$\frac{2x^{2}-8x-24}{3x^{2}-6x-9x+18}$$

Combine -6x and -9x to get -15x.

$$\frac{2x^{2}-8x-24}{3x^{2}-15x+18}$$