Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
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
We are given a system of equations: $x = \sqrt{y^2 - \frac{1}{16}} + \sqrt{z^2 - \frac{1}{16}}$ $y =...
System of EquationsSquare RootsAlgebraic ManipulationEstimation
2025/3/23
The problem asks us to find the inverse of the matrix $B = \begin{pmatrix} 2 & -1 & 0 \\ 1 & 3 & 1 \...
Linear AlgebraMatrix InverseGaussian EliminationPivoting
2025/3/23
The problem is to analyze the equation $4x^2 - 4y^2 - 2x + 2y + 1 = 0$. We need to determine the typ...
Conic SectionsHyperbolaCompleting the SquareEquation Transformation
2025/3/23