Solve 2+(x)x/x^2+4x+9

$$2 + ( x ) \frac { x } { x ^ { 2 } + 4 x + 9 }$$

Evaluate

$$\frac{3x^{2}+8x+18}{x^{2}+4x+9}$$

Short Solution Steps

Express x\times \frac{x}{x^{2}+4x+9} as a single fraction.

$$2+\frac{xx}{x^{2}+4x+9}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x^{2}+4x+9}{x^{2}+4x+9}.

$$\frac{2\left(x^{2}+4x+9\right)}{x^{2}+4x+9}+\frac{xx}{x^{2}+4x+9}$$

Since \frac{2\left(x^{2}+4x+9\right)}{x^{2}+4x+9} and \frac{xx}{x^{2}+4x+9} have the same denominator, add them by adding their numerators.

$$\frac{2\left(x^{2}+4x+9\right)+xx}{x^{2}+4x+9}$$

Do the multiplications in 2\left(x^{2}+4x+9\right)+xx.

$$\frac{2x^{2}+8x+18+x^{2}}{x^{2}+4x+9}$$

Combine like terms in 2x^{2}+8x+18+x^{2}.

$$\frac{3x^{2}+8x+18}{x^{2}+4x+9}$$

Differentiate w.r.t. x

$$\frac{2x\left(2x+9\right)}{\left(x^{2}+4x+9\right)^{2}}$$