SAT Math · Study & Practice

Rational Expressions

A rational expression is a fraction with polynomials on top and bottom. The SAT tests simplifying, the four operations and solving rational equations. This chapter covers simplification, multiplication, division, addition, subtraction and rational equations. Read each topic, try the problems with the hint ladder, then take the 8-question topic test.

Topics

1 Simplification 4 worked · 5 practice · 8-Q test Start → 2 Multiplication 4 worked · 5 practice · 8-Q test Start → 3 Division 4 worked · 5 practice · 8-Q test Start → 4 Addition 4 worked · 5 practice · 8-Q test Start → 5 Subtraction 4 worked · 5 practice · 8-Q test Start → 6 Rational Equations 4 worked · 5 practice · 8-Q test Start →

Chapter test

📝 Rational Expressions — Chapter Test

25 fresh questions · timed · full solutions

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Formula Reference Sheet

This chapter

Operations

Simplify	factor top and bottom, cancel common factors
Multiply	(a/b)(c/d) = ac/bd
Divide	(a/b) ÷ (c/d) = (a/b)(d/c)
Add/subtract	use a common denominator

Cautions

Restrictions	denominator ≠ 0 (exclude those x)
Solve equations	clear denominators, then solve
Check	reject answers that make a denominator 0

Digital SAT reference

Area & Circumference

Circle area	A = πr²
Circle circumference	C = 2πr
Rectangle	A = ℓw
Triangle	A = ½ b h

Volume

Rectangular box	V = ℓwh
Cylinder	V = πr²h
Sphere	V = 4⁄3 πr³
Cone	V = 1⁄3 πr²h
Pyramid	V = 1⁄3 ℓwh

Right triangles

Pythagorean theorem	a² + b² = c²
30°–60°–90°	sides x : x√3 : 2x
45°–45°–90°	sides s : s : s√2

Constants

Degrees in a circle	360°
Radians in a circle	2π
Angles of a triangle	sum = 180°