Solve 2((2x-3)(x+4))/(x-7)(x+3)

$$2 \frac { ( ( 2 x - 3 ) ( x + 4 ) ) } { ( x - 7 ) ( x + 3 ) }$$

Evaluate

$$\frac{2\left(2x-3\right)\left(x+4\right)}{\left(x-7\right)\left(x+3\right)}$$

Short Solution Steps

Apply the distributive property by multiplying each term of 2x-3 by each term of x+4.

$$2\times \frac{2x^{2}+8x-3x-12}{\left(x-7\right)\left(x+3\right)}$$

Combine 8x and -3x to get 5x.

$$2\times \frac{2x^{2}+5x-12}{\left(x-7\right)\left(x+3\right)}$$

Apply the distributive property by multiplying each term of x-7 by each term of x+3.

$$2\times \frac{2x^{2}+5x-12}{x^{2}+3x-7x-21}$$

Combine 3x and -7x to get -4x.

$$2\times \frac{2x^{2}+5x-12}{x^{2}-4x-21}$$

Express 2\times \frac{2x^{2}+5x-12}{x^{2}-4x-21} as a single fraction.

$$\frac{2\left(2x^{2}+5x-12\right)}{x^{2}-4x-21}$$

Use the distributive property to multiply 2 by 2x^{2}+5x-12.

$$\frac{4x^{2}+10x-24}{x^{2}-4x-21}$$

Expand

$$\frac{2\left(2x^{2}+5x-12\right)}{\left(x-7\right)\left(x+3\right)}$$

Short Solution Steps

Apply the distributive property by multiplying each term of 2x-3 by each term of x+4.

$$2\times \frac{2x^{2}+8x-3x-12}{\left(x-7\right)\left(x+3\right)}$$

Combine 8x and -3x to get 5x.

$$2\times \frac{2x^{2}+5x-12}{\left(x-7\right)\left(x+3\right)}$$

Apply the distributive property by multiplying each term of x-7 by each term of x+3.

$$2\times \frac{2x^{2}+5x-12}{x^{2}+3x-7x-21}$$

Combine 3x and -7x to get -4x.

$$2\times \frac{2x^{2}+5x-12}{x^{2}-4x-21}$$

Express 2\times \frac{2x^{2}+5x-12}{x^{2}-4x-21} as a single fraction.

$$\frac{2\left(2x^{2}+5x-12\right)}{x^{2}-4x-21}$$

Use the distributive property to multiply 2 by 2x^{2}+5x-12.

$$\frac{4x^{2}+10x-24}{x^{2}-4x-21}$$