Solve 2x^2-5x-12/4x^2+8x+3*x^2-16/2x^2+7x+3

$$\frac { 2 x ^ { 2 } - 5 x - 12 } { 4 x ^ { 2 } + 8 x + 3 } \cdot \frac { x ^ { 2 } - 16 } { 2 x ^ { 2 } + 7 x + 3 }$$

Evaluate

$$\frac{\left(\frac{x-4}{2x+1}\right)^{2}\left(x+4\right)}{x+3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{2}-5x-12}{4x^{2}+8x+3}.

$$\frac{\left(x-4\right)\left(2x+3\right)}{\left(2x+1\right)\left(2x+3\right)}\times \frac{x^{2}-16}{2x^{2}+7x+3}$$

Cancel out 2x+3 in both numerator and denominator.

$$\frac{x-4}{2x+1}\times \frac{x^{2}-16}{2x^{2}+7x+3}$$

Multiply \frac{x-4}{2x+1} times \frac{x^{2}-16}{2x^{2}+7x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\left(x^{2}-16\right)}{\left(2x+1\right)\left(2x^{2}+7x+3\right)}$$

Use the distributive property to multiply x-4 by x^{2}-16.

$$\frac{x^{3}-16x-4x^{2}+64}{\left(2x+1\right)\left(2x^{2}+7x+3\right)}$$

Use the distributive property to multiply 2x+1 by 2x^{2}+7x+3 and combine like terms.

$$\frac{x^{3}-16x-4x^{2}+64}{4x^{3}+16x^{2}+13x+3}$$

Expand

$$\frac{x^{3}-4x^{2}-16x+64}{\left(2x+1\right)\left(2x^{2}+7x+3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{2}-5x-12}{4x^{2}+8x+3}.

$$\frac{\left(x-4\right)\left(2x+3\right)}{\left(2x+1\right)\left(2x+3\right)}\times \frac{x^{2}-16}{2x^{2}+7x+3}$$

Cancel out 2x+3 in both numerator and denominator.

$$\frac{x-4}{2x+1}\times \frac{x^{2}-16}{2x^{2}+7x+3}$$

Multiply \frac{x-4}{2x+1} times \frac{x^{2}-16}{2x^{2}+7x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\left(x^{2}-16\right)}{\left(2x+1\right)\left(2x^{2}+7x+3\right)}$$

Use the distributive property to multiply x-4 by x^{2}-16.

$$\frac{x^{3}-16x-4x^{2}+64}{\left(2x+1\right)\left(2x^{2}+7x+3\right)}$$

Use the distributive property to multiply 2x+1 by 2x^{2}+7x+3 and combine like terms.

$$\frac{x^{3}-16x-4x^{2}+64}{4x^{3}+16x^{2}+13x+3}$$