Solve 19/x^2+10x+25+3/x+5

$$\frac { 19 } { x ^ { 2 } + 10 x + 25 } + \frac { 3 } { x + 5 }$$

Evaluate

$$\frac{3x+34}{\left(x+5\right)^{2}}$$

Short Solution Steps

Factor x^{2}+10x+25.

$$\frac{19}{\left(x+5\right)^{2}}+\frac{3}{x+5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+5\right)^{2} and x+5 is \left(x+5\right)^{2}. Multiply \frac{3}{x+5} times \frac{x+5}{x+5}.

$$\frac{19}{\left(x+5\right)^{2}}+\frac{3\left(x+5\right)}{\left(x+5\right)^{2}}$$

Since \frac{19}{\left(x+5\right)^{2}} and \frac{3\left(x+5\right)}{\left(x+5\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{19+3\left(x+5\right)}{\left(x+5\right)^{2}}$$

Do the multiplications in 19+3\left(x+5\right).

$$\frac{19+3x+15}{\left(x+5\right)^{2}}$$

Combine like terms in 19+3x+15.

$$\frac{34+3x}{\left(x+5\right)^{2}}$$

Expand \left(x+5\right)^{2}.

$$\frac{34+3x}{x^{2}+10x+25}$$

Differentiate w.r.t. x

$$\frac{-3x-53}{\left(x+5\right)^{3}}$$