Математика18 мин

Rational Expressions

Add, subtract, multiply, and divide expressions of the form $\dfrac{p(x)}{q(x)}$ — and watch the domain.

Four operations

Multiply: $\dfrac{a}{b} \cdot \dfrac{c}{d} = \dfrac{ac}{bd}$ — factor first, cancel.
Divide: flip second and multiply.
Add/subtract: common denominator first.
Always state restricted values where the denominator is zero.

Add

Simplify $\dfrac{1}{x} + \dfrac{2}{x+1}$ .

Жауап: $\dfrac{3x+1}{x(x+1)},\ x \neq 0, -1$

Cancel only after factoring. $\dfrac{x+2}{x}$ does NOT simplify to $\dfrac{2}{1}$ — that's cancelling across a sum.