Solve 2x^2-1/(x+1)(x+2)-2

$$\frac{ 2 { x }^{ 2 } -1 }{ (x+1)(x+2) } -2$$

Evaluate

$$-\frac{6x+5}{\left(x+1\right)\left(x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}.

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

Since \frac{2x^{2}-1}{\left(x+1\right)\left(x+2\right)} and \frac{2\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2x^{2}-1-2\left(x+1\right)\left(x+2\right).

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

Combine like terms in 2x^{2}-1-2x^{2}-4x-2x-4.

$$\frac{-5-6x}{\left(x+1\right)\left(x+2\right)}$$

Expand \left(x+1\right)\left(x+2\right).

$$\frac{-5-6x}{x^{2}+3x+2}$$

Expand

$$-\frac{6x+5}{\left(x+1\right)\left(x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}.

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

Since \frac{2x^{2}-1}{\left(x+1\right)\left(x+2\right)} and \frac{2\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2x^{2}-1-2\left(x+1\right)\left(x+2\right).

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

Combine like terms in 2x^{2}-1-2x^{2}-4x-2x-4.

$$\frac{-5-6x}{\left(x+1\right)\left(x+2\right)}$$

Expand \left(x+1\right)\left(x+2\right).

$$\frac{-5-6x}{x^{2}+3x+2}$$