Algebra

Algebra Guides

Clear, worked walkthroughs of the expression types that trip students up, each one taught slowly with the rule named at every step.

Showing 6 of 6 guides

Simplifying Fraction of fractions How to Simplify Complex Fractions (1/x + 1)/(1/x)

How to simplify complex fractions two ways: combine the top and bottom into single fractions then divide, or multiply every term by the LCD. Worked examples and a finished check.

8 min read Read the guide
Simplifying Keep the caveat Excluded Values and Domain Restrictions x ≠ −2, x ≠ 3

An excluded value is any input that breaks the original expression. Find every one from denominators, even roots, and logs, then write the domain the right way.

10 min read Read the guide
Simplifying Flip it How to Simplify Negative Exponents x⁻² = 1/x²

Learn how to simplify negative exponents the way they actually work: a negative power means a reciprocal, so x^-2 is 1/x^2. Rule, worked examples, and a finished check.

8 min read Read the guide
Simplifying The bridge Rational (Fractional) Exponents Explained x^(2/3) = ∛(x²)

A rational exponent is a root: the denominator is the root and the numerator is the power, so x^(2/3) is the cube root of x squared. Table, rules, worked steps.

8 min read Read the guide
Simplifying Clear the root How to Rationalize a Denominator 1/√2 → √2/2

How to rationalize the denominator: multiply the top and bottom to clear the radical, so 1/√2 becomes √2/2, and use the conjugate on a two-term bottom.

8 min read Read the guide
Simplifying Even roots bite Simplifying Radicals with Variables √(x²) = |x|

Simplifying radicals with variables works like numbers, but an even root needs absolute value: √(x²) = |x|, not x. Rules, the exponent shortcut, and examples.

8 min read Read the guide