Solve x^2+3x-21x/(x+2)^2-4

$$\frac { x ^ { 2 } + 3 x - 21 x } { ( x + 2 ) ^ { 2 } } - 4$$

Evaluate

$$-\frac{3x^{2}+34x+16}{\left(x+2\right)^{2}}$$

Short Solution Steps

Combine 3x and -21x to get -18x.

$$\frac{x^{2}-18x}{\left(x+2\right)^{2}}-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{\left(x+2\right)^{2}}{\left(x+2\right)^{2}}.

$$\frac{x^{2}-18x}{\left(x+2\right)^{2}}-\frac{4\left(x+2\right)^{2}}{\left(x+2\right)^{2}}$$

Since \frac{x^{2}-18x}{\left(x+2\right)^{2}} and \frac{4\left(x+2\right)^{2}}{\left(x+2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-18x-4\left(x+2\right)^{2}}{\left(x+2\right)^{2}}$$

Do the multiplications in x^{2}-18x-4\left(x+2\right)^{2}.

$$\frac{x^{2}-18x-4x^{2}-16x-16}{\left(x+2\right)^{2}}$$

Combine like terms in x^{2}-18x-4x^{2}-16x-16.

$$\frac{-3x^{2}-34x-16}{\left(x+2\right)^{2}}$$

Expand \left(x+2\right)^{2}.

$$\frac{-3x^{2}-34x-16}{x^{2}+4x+4}$$

Expand

$$-\frac{3x^{2}+34x+16}{\left(x+2\right)^{2}}$$

Short Solution Steps

Combine 3x and -21x to get -18x.

$$\frac{x^{2}-18x}{\left(x+2\right)^{2}}-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{\left(x+2\right)^{2}}{\left(x+2\right)^{2}}.

$$\frac{x^{2}-18x}{\left(x+2\right)^{2}}-\frac{4\left(x+2\right)^{2}}{\left(x+2\right)^{2}}$$

Since \frac{x^{2}-18x}{\left(x+2\right)^{2}} and \frac{4\left(x+2\right)^{2}}{\left(x+2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-18x-4\left(x+2\right)^{2}}{\left(x+2\right)^{2}}$$

Do the multiplications in x^{2}-18x-4\left(x+2\right)^{2}.

$$\frac{x^{2}-18x-4x^{2}-16x-16}{\left(x+2\right)^{2}}$$

Combine like terms in x^{2}-18x-4x^{2}-16x-16.

$$\frac{-3x^{2}-34x-16}{\left(x+2\right)^{2}}$$

Expand \left(x+2\right)^{2}.

$$\frac{-3x^{2}-34x-16}{x^{2}+4x+4}$$