simplify i/x+i/x^2 — step-by-step solution

The original denominators must be nonzero:

x \neq 0

Let's sum the fractions:

\frac{i}{x} + \frac{i}{x^{2}}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

\frac{i}{x} + \frac{i}{x^{2}}

\frac{i x^{2} + i x}{x x^{2}}

\frac{i x^{2} + i x}{x x^{2}}

Let's factor in

ℂ

i x^{2} + i x

You can write the expression in factored form:

i x \cdot (x + 1)

ⓘ The original denominator must remain nonzero. The fraction is simplified by dividing the numerator and the denominator by their common factor:

\frac{i x^{2} + i x}{x x^{2}}

\frac{i \cdot (x + 1)}{x^{2}}

▶Result:

\frac{i \cdot (x + 1)}{x^{2}}