Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
We are asked to simplify the following two expressions: (e) $\frac{2x^2 + 17x + 21}{(x+2)(x^2-9)}$ (...
PolynomialsSimplificationRational ExpressionsFactorization
2025/3/24
The problem asks to simplify the given rational expressions. We are given two expressions to simplif...
Rational ExpressionsFactorizationSimplificationAlgebraic Manipulation
2025/3/24
We are asked to express the rational function $\frac{4x-9}{(x-2)(x-3)}$ in partial fractions.
Partial FractionsRational FunctionsAlgebraic Manipulation
2025/3/24
The problem asks us to simplify rational expressions. We are given several fractions involving poly...
Rational ExpressionsSimplificationFactoring Polynomials
2025/3/24
The problem asks us to evaluate the expression $\frac{4}{x} + x$ when $x = \frac{1}{2}$.
Expression EvaluationSubstitutionFractionsArithmetic Operations
2025/3/24
Solve the inequality $6x + 13 < 5(2x - 3)$ for $x$.
InequalitiesLinear InequalitiesSolving Inequalities
2025/3/24
The problem is to solve the inequality $2(x-4) \geq 3x - 5$ for $x$.
InequalitiesLinear InequalitiesSolving Inequalities
2025/3/24
The problem is to express the complex number $\frac{4-i}{3+i}$ in the form $a+bi$, where $a$ and $b$...
Complex NumbersComplex ConjugateRationalizationArithmetic Operations
2025/3/23
The problem asks to decompose the rational function $\frac{8x-12}{x^2+3x-18}$ into partial fractions...
Partial FractionsRational FunctionsAlgebraic ManipulationFactorization
2025/3/23
Simplify the rational expression $\frac{8x-42}{x^2+3x-18}$.
Rational ExpressionsFactoringSimplification
2025/3/23