Solve f(x)=245/x^2+x/x+23

$$f ( x ) = \frac { 245 } { x ^ { 2 } } + \frac { x } { x + 23 }$$

Evaluate

$$\frac{x^{3}+245x+5635}{\left(x+23\right)x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and x+23 is \left(x+23\right)x^{2}. Multiply \frac{245}{x^{2}} times \frac{x+23}{x+23}. Multiply \frac{x}{x+23} times \frac{x^{2}}{x^{2}}.

$$\frac{245\left(x+23\right)}{\left(x+23\right)x^{2}}+\frac{xx^{2}}{\left(x+23\right)x^{2}}$$

Since \frac{245\left(x+23\right)}{\left(x+23\right)x^{2}} and \frac{xx^{2}}{\left(x+23\right)x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{245\left(x+23\right)+xx^{2}}{\left(x+23\right)x^{2}}$$

Do the multiplications in 245\left(x+23\right)+xx^{2}.

$$\frac{245x+5635+x^{3}}{\left(x+23\right)x^{2}}$$

Expand \left(x+23\right)x^{2}.

$$\frac{245x+5635+x^{3}}{x^{3}+23x^{2}}$$

Differentiate w.r.t. x

$$\frac{23x^{3}-490x^{2}-22540x-259210}{\left(x+23\right)^{2}x^{3}}$$