Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem defines a binary operation $*$ on the set of real numbers $R$ such that $a * b = a + b +...
Binary OperationReal NumbersAlgebraic ManipulationFractions
2025/7/6
A binary operation $*$ is defined on the set of real numbers $R$ by $a * b = 4a^2b$. We need to eval...
Binary OperationReal NumbersAlgebraic Manipulation
2025/7/6
A binary operation $*$ is defined on the set of real numbers $R$ by $a * b = a + a^2b$. Evaluate $\f...
Binary OperationReal NumbersExpression Evaluation
2025/7/6
The problem asks us to simplify the expression $y = \frac{2}{x^2 - 9} + \frac{1}{x-3}$.
Algebraic simplificationRational expressionsFactorizationCommon denominator
2025/7/6
The problem states that $y$ is the sum of two quantities. One quantity varies directly as $x^2$, and...
Algebraic EquationsDirect and Inverse VariationSystems of Equations
2025/7/6
The problem has two parts. (a) We need to express the sum of two fractions, $\frac{3}{2}$ and $\frac...
FractionsSimplificationFormula ManipulationSubstitutionSolving for a Variable
2025/7/5
The problem is to simplify the expression $\frac{3}{2} + \frac{4x-1}{3}$.
Algebraic ExpressionsFractionsSimplificationVariables
2025/7/5
The problem states that four numbers are in the ratio 11:19:5:7. The sum of these four numbers is 22...
Ratio and ProportionLinear EquationsWord Problem
2025/7/4
The problem states that four numbers are in the ratio 11:19:5:7. The sum of these four numbers is 2...
Ratio and ProportionLinear EquationsProblem Solving
2025/7/4
The sum of two numbers $p$ and $m$ is 12, and $p^3 + m^3 = 360$. We need to find the value of $pm$.
Algebraic EquationsPolynomialsFactoringProblem Solving
2025/7/4