Solve 5/2x+611/2x^2+12x+18

$$\frac { 5 } { 2 x + 6 } \frac { 11 } { 2 x ^ { 2 } + 12 x + 18 }$$

Evaluate

$$\frac{55}{4\left(x+3\right)^{3}}$$

Solution Steps

Multiply \frac{5}{2x+6} times \frac{11}{2x^{2}+12x+18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 11}{\left(2x+6\right)\left(2x^{2}+12x+18\right)}$$

Multiply 5 and 11 to get 55.

$$\frac{55}{\left(2x+6\right)\left(2x^{2}+12x+18\right)}$$

Use the distributive property to multiply 2x+6 by 2x^{2}+12x+18 and combine like terms.

$$\frac{55}{4x^{3}+36x^{2}+108x+108}$$

Differentiate w.r.t. x

$$-\frac{165}{4\left(x+3\right)^{4}}$$