Solve x+2/x+5divx^2+4

$$\frac{ x+2 }{ x+5 } \div { x }^{ 2 } +4$$

Evaluate

$$\frac{4x^{3}+20x^{2}+x+2}{\left(x+5\right)x^{2}}$$

Short Solution Steps

Express \frac{\frac{x+2}{x+5}}{x^{2}} as a single fraction.

$$\frac{x+2}{\left(x+5\right)x^{2}}+4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{\left(x+5\right)x^{2}}{\left(x+5\right)x^{2}}.

$$\frac{x+2}{\left(x+5\right)x^{2}}+\frac{4\left(x+5\right)x^{2}}{\left(x+5\right)x^{2}}$$

Since \frac{x+2}{\left(x+5\right)x^{2}} and \frac{4\left(x+5\right)x^{2}}{\left(x+5\right)x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x+2+4\left(x+5\right)x^{2}}{\left(x+5\right)x^{2}}$$

Do the multiplications in x+2+4\left(x+5\right)x^{2}.

$$\frac{x+2+4x^{3}+20x^{2}}{\left(x+5\right)x^{2}}$$

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

$$\frac{x+2+4x^{3}+20x^{2}}{x^{3}+5x^{2}}$$

Expand

$$\frac{4x^{3}+20x^{2}+x+2}{\left(x+5\right)x^{2}}$$

Short Solution Steps

Express \frac{\frac{x+2}{x+5}}{x^{2}} as a single fraction.

$$\frac{x+2}{\left(x+5\right)x^{2}}+4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{\left(x+5\right)x^{2}}{\left(x+5\right)x^{2}}.

$$\frac{x+2}{\left(x+5\right)x^{2}}+\frac{4\left(x+5\right)x^{2}}{\left(x+5\right)x^{2}}$$

Since \frac{x+2}{\left(x+5\right)x^{2}} and \frac{4\left(x+5\right)x^{2}}{\left(x+5\right)x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x+2+4\left(x+5\right)x^{2}}{\left(x+5\right)x^{2}}$$

Do the multiplications in x+2+4\left(x+5\right)x^{2}.

$$\frac{x+2+4x^{3}+20x^{2}}{\left(x+5\right)x^{2}}$$

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

$$\frac{x+2+4x^{3}+20x^{2}}{x^{3}+5x^{2}}$$