add the fractions 4/x and (x+1)/(x-5)

Let's sum the fractions:

\frac{4}{x} + \frac{x + 1}{x - 5}

\frac{4 \cdot (x - 5) + (x + 1) \cdot x}{x \cdot (x - 5)}

ℹ

4 \cdot (x - 5)

4 x - 20

‖

(x + 1) \cdot x

x^{2} + x

\frac{(4 x - 20) + (x^{2} + x)}{x \cdot (x - 5)}

ℹ

4 x

- 20

+ x^{2}

+ x

5 x - 20 + x^{2}

\frac{5 x - 20 + x^{2}}{x \cdot (x - 5)}

▷Result: $\frac{x^{2} + 5 x - 20}{x \cdot (x - 5)}$